проверьте мой английский

Я бы сказал Did you study at school well ?

Я бы оставила первый вариант.

I don't know what you mean by this
sentence. "Study" is something you do at home after school. The other meaning of "study," is in the general sense of being in school. That naturally would not apply here because it's not something you do over the course of one day. So I can't imagine what this means.

Then "Did you learn well at school?". The meaning is whether you were a good pupil at school.

Aha!

Obviously, if you're in school, you're there to learn. Similarly, if you're at work, you're there to work. So in such cases, we just say have a good day at school/work, and that means to be successful at everything you do in those places.

But it's not for one day but in general. For example, adults talk and one of them asks the other if he was good at school. Were you good at school?

In that case, Were you a good student?

Were you a good pupil at school? Students are usually at colleges and universities, aren't they?

Student here is general for someone who's studying, and HOW they studied.

Were you a good student at school?

ты хорошо учился в школе?(исходное предложение)