What does this capacitor do?

Capacitor belongs to a pretty big main power rail and does what all capacitors do, stores and smooths power for the ICs on that rail. The Mac can work and be used even without it given the big number of other capacitors on the same rail but it could be replaced by soldering a good one in its place if you wish so.

Liquid on a board can bring along all sorts of issues, it’s not possible to give a straight answer as to why you have full speed fans without testing the board and trying replacing parts. It may simply be a bad cable, I/O board, trackpad as well as many other things on the board itself.