2 Tom thinks chat shows and period dramas are both boring.
INTERESTING / BORING
a Tom thinks chat shows are
period
dramas. (just)
b Tom thinks period dramas aren't
chat shows. (more)
Очень нужна

1. The hostages were rescued (сказуемое в страдательном залоге) without a shot being fired (обстоятельство - при произведении выстрела).
2. I wish my refrigerator would stop making (составное сказуемое - прекратить делать) that terrible noise. You can’t hear anyone speaking.
3. The results received (определение - какие результаты) were of great importance for further work.
4. People living (определение - какие люди) in Japan have some customs different from ours.
We had already had lunch when he came.

Перевод очень хороший. "T" и "F" я бы расставила так же.

А в вопросах предложу пару правок:

У Вас: 3. Does American English have absorbed many words from the languages of immigrants? Это общий вопрос к предложению:
American English has absorbed many words from the languages of immigrants. Тут время Present Perfect, поэтому вс глагол в общем вопросе должен быть другим. Правильно так:
Has American English absorbed many words from the languages of immigrants?

4. Rodeo and tornado are a Spanish words, aren’t they?
Spanish words - множественное число, поэтому артикль "а" уберите.
Правильно: Rodeo and tornado are Spanish words, aren’t they?

 5. Which parts of America was controlled by France and Spain?
parts of America - тоже множественно число, поэтому глагол не was, а were. Правильно: Which parts of America were controlled by France and Spain?

6. Did the word hamburger came from German? Тут вс глагол did "забирает на себя" время, основной глагол должен быть в первой форме. Правильно: Did the word hamburger cоme from German?

8. What for did Europeans learn words from the local languages of America? Не уверена, но как будто "what for" скорее неформальный, разговорный оборот. Лучше так: Why did Europeans learn words from the local languages of Noth America?

9. Native Americans also worked as guides, leading the European traders [around the country], didn’t they? Тут хочется добавить "где именно водили".