Perplexing questions

1-Find the mistakes in each of the following sentences then write it correctly:
1- Tom doesn't think you can finish in time, can't you?
2- Because he had been tired, he refused to go out, hadn't he?
3- Tom fell asleep while he was watching the film, wasn't he?
4- I didn't imagine he didn't succeed, did he?
My answers:
1-Tom doesn't think you can finish in time, doesn't he? Or : can you?
(In fact, I am not sure of my answer to this sentence. Is there a difference between sentences beginning with : I /We think + sentence and sentences beginning with: He/She/You/They think + sentence in tag questions? I would appreciate it if you told me the rule.
2-Because he had been tired, he refused to go out, didn't he?
3-Tom fell asleep while he was watching the film, didn't he?
4-I didn't imagine he didn't succeed, didn't he? Is it possible to say "didn't I ?
2- Choose the correct answer:
1- The ceiling of the room doesn't look very safe. It looks as if it……fall down.
a) Will b) is going to
My answer is (b) is going to. However, I feel that "will" is acceptable?
2- Rewrite the following sentence using the words in brackets:
1- Her baby will be born in October. (is)
My answer is : He baby is to be born in October.
Is it possible to say that: She is going to have a baby in October?