1. Look! Somebody is climbing up that tree over there. - OK (верно)
2. Can you hear those people? What are they talking about? (говорят в данный момент - Present Continuous)
3. Do you believe in God? (глаголы восприятия в Continuous не используются)
4. Look! That man is trying to open the door of your car. (действие происходит в момент речи)
5. The moon goes round the earth. - OK
6. I think it would be a good idea to leave early. (тоже глагол восприятия)
7. The government is worried because the number of people without job is increasing. - OK
8. I usually go to work by car. (Это регулярное действие в настоящем - Present Simple)
If I knew that the traffic lights were red, I would have stopped.
The newspaper would print the story if it were true.
If I had known that you were in hospital, I would have visited you.