Hello Mari Kim There is a good answer to that. In your example "he is a good student in school" you explain that the person is a student. 'Student' is the noun here, serving as an object. The adjective "good" describes what kind of student he is: a good one. In your other example "I was pretty good at studying" you use the verb "studying" as a noun, which we call a gerund. The purpose of this is that you focus the attention to the act of studying instead of to the person. He's a good student. But if he's "good at studying" he isn't just intelligent, but his method of studying is good. I hope this helps.

The sentence is correct. You can be good at anything, and studying is not an exception :)

It makes sense. It is just in the past tense (specifically the past simple). While the later examples you gave were in the present tense.