1. 私にはまだ例の反日感情があったが、それよりも、恥ず かしながら、まず山へ行って人並な生活をしたいという 欲望のほうが強かった。
My translation: "I still had the usual anti-Japanese sentiment, but nevertheless, and although I was shy, I above all had a strong desire to go to mountains and live an ordinary life."
a) In what sense do you think まだ is used? I translated it as "still", but I don't really understand why in 1940 he would use the word "still" in reference to anti-Japanese sentiment amongst Americans, assuming that's what he's referring to. Maybe in 1960, yes.
b) In what sense is 例の used?
c) Is 恥ずかしい more like "shy" or "embarrassed"?
d) How would you translate 人並な生活 here?
a) The speaker had had the anti-Japanese feelings in the past and he still had it.
Since it is not clear why he had that feelings - based on his past experience or the general tendency in the place he was living, it is hard to tell whether it was 1940 or 1960.
Considering the Japanese-American internment was in 1942, it is possible that there was already some anti-Japanese sentiment but I'm not sure.
b) 例の is used to refer a particular thing that is already known/understood between the speaker and those who are being spoken. It can be translated as "the" or "that".
Obviously his anti-Japanese feeling was already mentioned before this sentence.
c) 恥ずかしい in 恥ずかしながら is "shame".
I'm ashamed to tell/say/admit...
d) 人並み literally means "same level as people/others".
So your translation "ordinary" fits well. Alternatively, "normal" or "decent" can be used.
2. 別荘に着いてみると、家庭教師は既に来ていて、果樹園 で果物を折っていた。
My translation: "When we arrived at the villa, the tutor had already come (i.e. arrived), and was picking fruit in the orchard."
What meaning does みる have here? Is it literally referring to their seeing the villa?
~てみる is an expression for "to do something for a try/change/to see what it is like".
It is also used to express "to do something then see/realize/find (the result, fact, etc)"
In this case it is the latter.
3. 国籍上はアメリカ人でも、英語はほとんどできなかった わけで、それがかえって日本語を習う上ではよかったよ うだ。
My translation: "Although he was an American citizen, he spoke hardly any English, but despite this, it was good learning Japanese (from him)."
Even if this is close, I don't exactly understand what わけ, 上 or よう mean in this context.
I'm also not very sure about それがかえって, which I guessed to mean something like "despite this"?
わけ is used to say the conclusion. Maybe there is some explanation about himself, which is followed 国籍上はアメリカ人でも英語はほとんどできなかった.
This わけ does not have to be always translated, I think, but if I dare to put into words, "that is..." "which is to say..." for instance.
上で has several meanings but here it means the same as ため.
日本語を習う上では=日本語を習うためには to learn Japanese
よう means assumption by the speaker. It seems, I guess, I think, etc.
かえって means "contrary to the expectation".
What expectation was there is not clear, but the possibility is:
Normally a person who has American citizenship is supposed to be able to speak English fluently and inability in English language is usually considered as disadvantage.
But in this particular situation, being not able to speak English helps learning Japanese.