Questions as a new law student

I’m from Maharashtra for context. I have recently joined law college and am curious about 2 things First, I want to know how case laws/precedents are presented to court? Is it like in moots? Are they supposed to be incorporated in pleading text itself, Like a citation or an extract? Or are they separately printed and submitted with full text? What's the procedure of using them? Are they submitted beforehand along with the pleadings as attachment, or can you bring them up during arguments only? Are the opponent's legal team notified about them too? Another thing I want to know is that we see huge luxurious firms like Khaitan, and also on the other end, small Individual advocate's offices on the streets, who occasionally get clients. My query is, what causes this disparity? If all lawyers at a minimum should know how to research and draft, then what distinguishes a huge law firm from a local advocate? any skill issue, special knowledge, contacts etc? Last question is that at which stage is the case laws as aforementioned presented during a trial? I would really love detailed answers about them, as I've been curious for a while.