Will be visiting coimbatore :) so need help planning itinerary and travel (to amrita university).

Hi Everyone, I will be visiting coimbatore around the later half of december for an event, and need some help in planning local travel. 1. I will be landing at the airport at night, so what is the best/most efficient way I can reach Amrita Vishwa Vidhya Peetham Univeristy from there? Also, what are the timings of the public transport that I can take from the airport? 2. When I have to get back from the university will it be possible to get a cab or something at night/early morning(sometime around 2AM to 3 AM)? Also what is the best way to reach bangalore from coimbatore? I would presume it's through train, but it's a long waiting list unfortunately :(.