I just realized I'm about to finish Winterhold college mainline quest. I thought it would be longer so I thought I would do its sidequests a bit later. Will it be possible to finish all of its sidequests (like getting the books, or helping fellow novice mages etc.) after I become the Archmage or should I finish them all before that?
You can still do the sidequests later. You get a few extra side quests after you've become the archmage. But for the purposes of immersion, I would do the sidequests before finishing its main quest. It is a bit strange to be bossed around when you are the archmage. Also, the supply of sidequests is quite boundless, as some of them are radiant (automatically generated), so if you are trying to do all of the side quests you will find this is quite impossible.