Sure! Here are the sentences rewritten using conditional structures and inversion:

1. I won’t come unless they invite me.
→ Unless invited, I won’t come.

2. He failed the exam because he didn’t revise all his lessons.
→ Had he revised all his lessons, he wouldn’t have failed the exam.

3. Please turn on the air-conditioning if you arrive at the office earlier than I do.
→ Should you arrive at the office earlier than I do, please turn on the air-conditioning.

4. The children don’t go to school in the snowy weather.
→ If it snows, the children won’t go to school.

5. You must tell me the whole truth, or I won’t help you.
→ Unless you tell me the whole truth, I won’t help you.

6. The car breaks down so often because you don’t take good care of it.
→ Were you to take good care of the car, it wouldn’t break down so often.

7. He is very bad-tempered; that’s why his wife left him soon after marriage.
→ Had he not been so bad-tempered, his wife wouldn’t have left him soon after marriage.