Can you generally find which terminal(s) an airline uses from the airports website.

For airports where an airline uses multiple terminals, which one is used for a specific flight is generally not known until several hours before the flight is scheduled to leave, and even then it can change within that time for several reasons.

Even then, you specifically mentioned for pickup/dropoff/parking/etc - to some extent these aren't related to the terminal that the flight actually departs from, they are related to the location of the check-in counters and baggage claim areas, which are generally centralized (per airline) even when an airline uses multiple terminals (there are exceptions, but they aren't common)