I.
1) He can't read hard texts
2)Can I go in?
3)Can I go to the zoo tomorrow?
4)I have to translate two excersises
5)We'll be allowed to watch this movie next week
6)I couldn't speak English three years earlier
7)Mom, can I play football tomorrow?
8)I will not be allowed to take a test next lesson
9)She should done the homework in time
10)You shouldn't help him. He must do it himself
II.
1)I can't sing but I can dance
2)Can I take your pen? I can't find my own
3)You should go to school, you must study
4)She could/couldn't ski when she was young
5)The weather was hot last summer. Can you swim?
6)will be able (раз to стоит, но может опечатка какая)
III.
1) I had to
2) Can you write a letter tomorrow? (can может относится и к будущему)
3) shouldn't
4) could
5) will you have to (?вроде так)
6) May he close / Will he be allowed to close (оба варианта подходят)
7) He won't be allowed to
8) She might read
9) You had to
10) May I take / will I be allowed to take (оба варианта, но 2й более формальный, 1й подходит больше)
Блин, вроде верно. Ох, уж эти модальные [email protected]#$!!! However, good luck!