Near the beginning of episode 2 of Band of Brothers one of the captured Germans is an American who "answered the call of the motherland" before the US joined WW2

(Edited to add Searocksandtrees's links to make this a more useful bag o' links.)

If you do a search in this group for

band of brothers

you will find so very many postings where this question was asked.

Most have been archived, though, so you can't followup there. So this is not to discourage further questions, rebuttals, or points.

In "Band of Brothers", we see a German soldier who is, in fact, an American who went to join the war for Germany in 1941. Did this occurence ever happen and if so, how common was it?: don't bother, because this just points to another answer.
In episode 2 of Band of Brothers there's an American fighting for the Germans because "[His] family answered the call. All true Aryans should return to the Fatherland" Did that actually happen? If so, how widespread was it?: /u/Searocksandtrees pointed to 7 previous threads. Most don't have "Band of Brothers" in their titles, so I'll copy them here for convenient reference:
... Did any non-Germans join the Nazi Army during WWII?: several answers.
... I keep hearing about people from other countries who were forcibly conscripted to fight for the Nazis or Soviets in WWII. Historically, what was conscription like in Europe?: mostly about conscription in general, but /u/vonadler wrote about Volksdeutsche, but also conscription of other nationalities in WWII.
... What is the history of Americans serving under the Nazis during WW2? Were there any reports of American soldiers committing treason and fleeing for Germany?: one answer by /u/leicanthrope, with interesting bits on a Norweigan document on nationalities of German soldiers showing one American, and "Brandenburgers", infiltrators in the Battle of the Bulge who tried to bollux things up on the American side.
In the series Band of Brothers during the post D-Day operations one of the German prisoners turns out to have been an American who had gone to Germany at the beginning of the war. Was this common?: /u/magicjj7 had the top but brief reply, and /u/alexschmitz reported on a letter held in his family.
In Band of Brothers, there is a German soldier born and raised in Oregon, but is serving in the Nazi military because his family "answered the Aryan call," or something along those lines. Was there an actual call to German, "Aryan" descendants to return home?: /u/JohnMLTX pointed to books and gave background, /u/TitusBluth gave more details, and /u/Georgy_K_Zhukov gave more.
How many US citizens of German descent fought for Germany in WW2? Thinking of this scene in Band of Brothers where the American soldiers meet a German POW... who speaks perfect English.: /u/coinsinmyrocket gave a lot more info, unfortunately including "So far as I can tell, no hard number exists in regards to the number of American citizens (either by birth or naturalization) who fought for Nazi Germany."
In the Miniseries Band of Brothers, in the second episode easy company comes across some captured germans, one of them was an american. is this accurate and if so were there many americans in the german army?: ignore. It's just a reprise of #2 above.
What fate awaited the Americans who volunteered for service in the Wehrmacht?: a little more info from /u/ctesibius, noting British soldiers, and possible suppression of info.
In the second episode of Band of Brothers, one of the characters encounters an American-born German soldier. Are there any actual records of Americans with German ancestry returning to Germany to fight for the Axis powers?: /u/Superplaner points to a book, and then provides a table of data.
In Band of Brothers they come across an American POW who was fighting for Germany. How many foreigners (from non axis countries) fought for the Nazi's and what did they do after the war/ how were they treated?: /u/Searocksandtrees's list again.