For 1, both are possible. Second is more common and could be ambiguous. (Use ‘had’ if finished in the past. Using ‘had’ or ‘have’ is possible if it’s the present. ‘Have’ is better then if not otherwise clear from context.) For 2, you can use ‘can’ as follows: She can read well even though she hasn’t started school yet. Saying ‘starting school’ doesn’t sound right if it hasn’t happened.

1. Yes, or go with him. 2. Could is better if she has already started school. If she hasn't started yet, then can.

All four sentences are correct. The first two mean the same thing. The third and fourth have very different meanings. #3: She is not in school yet. She can learn to read well now before she starts school. #4: She is in school now. She knew how to read well before she started school.