These are the four reactions I would offer to the four above cases:

Language
About 180,000 is the conservative estimation for the number of first-generation immigrants from all of the German countries who fought for the Union. Many of these did not speak a word of English when they arrived. Of course chances are that by today that situation has reversed itself, and now it is you who doesn't speak a word of German.
The worst you could do now at reenactments or during living history representations, is to use an amalgam of the ususal phrases and swear words as heard on TV. This language of Hogan's Heroes has as much right to be in Civil War reenacting as blue jeans and BB guns. If you are really hardcore and will also lose 20 pounds of weight to be in the correct shape for Appomattox, you might think about attending language courses, getting yourself an "English-German" dictionary, or even travelling to Germany for a full immersion program. Not a bad idea, however I would recommend saving yourself the pain and the effort. Nineteenth century German was a fluctuating, unstable thing, with no clear standard orthography or pronunciation. Most of the farmers and common laborers who made up the majority of the immigrants would have spoken different dialectal variants, depending on where they were from. The intellectuals and skilled workers who made up the bulk of the 48er refugees, on the other hand, would have been fluent in at least one foreign language (possibly English, but more commonly French).
Your best option, in my opinion, is to stay where you are. Do not attempt to "Germanize" your language. Tell your audience at living history demonstrations that you are portraying a German immigrant who would have spoken about as much English then as you (or they) speak German now. Ask them to try and think themselves into his situation, linguistically. What is more important than to actually know the language is to know the customs, and the personal, political, and social history of your man (or woman, for that matter).
One thing that works wonders: If you have a singing voice, join your local German-American Singing Society, or else get yourself some records with traditional German folk songs. The present 15oth anniversary celebrations of the 1848/1849 revolutions have already brought forth some useful CDs (see bibliography below). "Oompah music" is not the same as traditional German folk singing! Maybe some members of the choir will join you in your hobby, and should I ever get to the U.S. again and hear you guys sing the old "Ännchen von Tharau", the "Morgenrot" or Ferdinand Freiligrath's "Weise von Marseille," I'll happily join in. Never sing "I fights mit Sigel" or "Corporal Schnapps!" Those songs made intentional fun of the German soldiers, and I wouldn't want to know how many eyes were blackened because of them, notably in the Army of the Potomac after Hooker and Howard had exculpated themselves at the expense of the Germans in the XI Corps after the Chancellorsville desaster.
If you cannot sing, recite poetry: Friedrich Schiller (d. 1805) was still the most popular German poet of the period. "Forty-Eighters" would have recited Hoffmann von Fallersleben, Georg Herwegh, or Heinrich Heine, the more conservative majority would have favoured Ludwig Uhlandt or Ernst Moritz Arndt 1.). Schiller they all agreed on; the Schillerfests of 1859 were huge all-out affairs, and celebrated all through the country including the California gold mining towns! 2.)

Looks
I would not do anything special about that either. Contrary to 1860s newspaper article claims, Germans are no more lop-eared than other ethnicities. Still, should your looks be those described above under 2., tough. Of all the persons on period Cartes-De-Visite I have studied, only the old communist August Willich and the proto-anarchist Hermann Ulffers appear to have stubbornly retained the full beard and long hair the revolutionists sported in 1849. Most of the others show the same beards and haircuts as everybody else. Most of those under 25 years of age are clean shaven. Do not turn up your whiskers, or grew a crew-cut! This fashion can clearly be traced to the Wilhelminian epoch, and does not appear before the 1890s. Likewise, immigrant women went with the local/regional fashion wherever possible.
As far as clothes are concerned, few if any emigrants, (let alone the exiles,) seem to have taken along their "Trachten" from home, so don't wear the "traditional" Lederhosen you bought years ago at the Oktoberfest in Munich. Even the pants of Captain Hubert "Lederhose" Dilger of Chancellorsville and Gettysburg fame (Battery 1, 1st Ohio Artillery) were not your typical Bavarian monstrosities, but doe-skin "breeches", going down to below the knees. A very recent immigrant might still wear such breeches, and the typical wide-sleeved working shirt, but we are talking a soldier's impression here, so I shall stop. In Union uniform, the German was pretty much indistinguishable from the rest; no harps, no kilts. The Garibaldi Guards (more Swiss, Germans, and Austro-Hungarians than Italians) wore their special uniforms of course, and Franz Sigel's 3rd Missouri Infantry first received a uniform shirt that appears to have been designed and cut to resemble the "Freischarenblusen" of 1849. Other than that, the only special adornment you might consider wearing (ball and parade use only) if your impression is that of a democrat refugee is a German national black, red, and gold cockade. In its period from, it had the yellow band outside and the black in the center.

Background, customs, and behavior
There were 38 different little Germanies in the 1850s. So it would be a good idea to research your man or woman, trace them to a place, and then look into an old encyclopedia for additional information on that particular kingdom, dukedom, archdukedom, count-dom (countdom??), or whatever. If Michael Bacarella had done at least that much, he would have spared himself and us the embarrassing misspelling of the German states 3.) and provinces which mar his otherwise interesting book on the 39th New York. If you are interested in local customs, there is a much neglected contemporary source which unfortunately appears never to have been translated into English: Eduard Duller, Das deutsche Volk in seinen Mundarten, Sitten, Braeuchen und Trachten. 4.) Its diction is antiquated and nationalistic, but it gives you a good idea of the different peoples inhabiting Germany at the time, regional dialects, interesting customs, and local folklore that an immigrant would have at least remembered if not continued.
As far as manners and societal behavior are concerned, some differences are notable. There is, for example, no reference whatsoever to spitting in public in the 1852 edition of the German Knigge. It simply wasn't done. Women were, if my reading is correct, more likely to be treated as equals, and the focus of the book is more on the art and development of communicative skills than on mannerisms.

Generally
The average German immigrant soldier of the american Civil War is literate and has an above average education, even if he does not speak English. If older than thirty, he probably served before, usually as a conscript in one of the German armies. Conditions there were tough and the drill very strict, so he tends to be rather obedient, effective, and good at drilling (not that he likes it more than anybody else).
Politically speaking, he is most likely to be a free-soil, free-labor democrat who reluctantly voted Republican in 1862, and for Lincoln in 1864. The memories of "Know-Nothing" and nativist terrorism run deep. Many of them were decidedly anti-slavery, and will easily fraternize with African-Americans. As many have a profound hatred of aristocrats, European or Southern, and will forage with a vengeance. They are not as religious as their American counterparts. At least two German regiments founded "Free Churches" in order to have freethinkers as their "Chaplains" (and both Albert Krause for the 12th Missouri and "Red" Becker with the 8th New York did a good job). Freethinker or not, the average German would have thought the Americans bigoted, and overly pious.
If possible, the immigrant community (likewise the soldiers) would celebrate and enjoy their Sundays with extended walks, sports, picnics, and in beer-gardens. This is where, finally, the fun of portraying a German immigrant soldier comes in. Yes, drinking and even brewing lots of beer is German! Even those immigrants from the wine-growing areas in Baden, Frankonia, Wurttemberg and the Palatinate would make no exception. Also, in the nineteenth century sauerkraut was far more widespread as a staple foodstuff than it is today. If you can, procure a small stone vat, fill it with sauerkraut, put a wooden lid on it, cover it with a cloth, and tie the cloth-covered lid to the vat. Transport to reenactments like that, and eat the sauerkraut either raw (best nutritional value) or cook it up with your salt pork ration and some potatoes and onions.
Enjoy ­ and have fun with your impression.

Research Ideas For Your German Impression:
To get an impression what immigrant life was like, I would recommend places like the Missouri Historical Society Museum in St. Louis, 5.) or the Deutschheim settlement, also in Missouri. Helpful sources on the German immigrant and notably on the 48er refugee in the Civil War era are the books by Wittke, Burton, Zucker, Brancaforte, and Lonn (in that order) 6.). Wilhelm Kaufmann's book on Germans in the Civil War 7.), however, on which all of the above draw to some extent, is horrifyingly inaccurate in many respects, but notably in the biographical data he gives of many German soldiers.
By far the best book source is Bruce Levine's, The Spirit of 1848 8.), but he covers the war itself only in passing. The website to browse is Robert Shea's German-American sites and links at www.serve.com/shea/germusa/germusa.htm. I have placed a list of some 140 "Forty-Eighters" and a short annotated research bibliography on the net. Also on this page: a handful of German Civil War songs from the 1860s! A handsome CD with songs of the 48 is "Die Gedanken sind frei" by D'Gelfieler (I know, I know...) available from Gelfieler-Verlag, Jahnstrasse 8, D-77948 Friesenheim, Germany, fax: +49 7821 61472, for only $11, plus shipping costs.

Notes:
1.) A contemporary bilingual edition that may give you an idea of the German poetry and authors that were popular in the U.S. is Alfred Baskerville Jr., The Poetry of Germany, (New York, 1854).

2.) See, for example, "Schiller celebration at Columbia", Tuolumne Courier, Oct.1, 1859. Thanks to Sharon Grout, Columbia Park Ranger, who really went out of her way to get this information for us.

3.) The other embarrassing thing about Michael Baccarella's, Lincoln's Foreign Legion: The 39th New York Infantry, Garibaldi Guards (Shippensburg, PA: White Mane, 1996), is its asinine title. What Bacarella calls a "Foreign Legion" was closer to the International Brigades of the Spanish Civil War - as were many of the early-war, all-ethnic regiments. The appendix lists the countries and cities of origin of the enrolled officers and men. Unfortunately, Bacarella apparently had nobody to correct the misspellings and geographically inaccurate renditions of most German-language place names.

5.) Thanks to Doug Harding, St. Louis, for his advice, guidance, and hospitality!

6.) Carl Wittke, Refugees of Revolution: The Fourty-Eighters in the United States, (New York, 1952); William Burton, Melting Pot Soldiers: The Union's Ethnic Regiments, (Ames, IA: Iowa State UP, 1988); A. E. Zucker, ed., The Fourty-Eighters: Political Refugees of the German Revolution of 1848, (New York, Columbia UP, 1950); Charlotte Branceforte, ed., The German Forty-Eighters in the United States, (NY: Lang, 1989); Ella Lonn, Foreigners in the Union Army and Navy, (New York: Greenwood, 1969 (1951)).

7.) Wilhelm Kaufmann, Die Deutschen im amerikanischen Bürgerkriege, (München: Oldenbourg, 1911).

8.) Bruce Levine, The Spirit of 1848. German Immigrants, Labor Conflict, and the Coming of the Civil War. (Urbana/Chicago: U. of Illinois Press, 1992).