Here are the corrections for each sentence:

1. **Sentence**: Michael fancies to travel, so whenever he is free, he goes around the city and enjoys the outdoors.
**Correction**: Michael fancies traveling, so whenever he is free, he goes around the city and enjoys the outdoors.

2. **Sentence**: I think playing sports are good for our mental and physical health.
**Correction**: I think playing sports is good for our mental and physical health.

3. **Sentence**: My dad loves cooking meals for our family. He is a good cooker.
**Correction**: My dad loves cooking meals for our family. He is a good cook.

4. **Sentence**: I am not onto driving to work at rush hour because the traffic is heavy.
**Correction**: I am not keen on driving to work at rush hour because the traffic is heavy.

5. **Sentence**: Would you like trying my home-made pizza?
**Correction**: Would you like to try my homemade pizza?