For instance, do you always have to use the same fingers to play the same keys or could you use whatever fingers you want?
No it’s not like typing. Generally your sheet music (atleast lower level music) will offer finger numbers to help you move around the keyboard in an efficient way. Having a teacher to guide you in this process is really important so that you develop good fingering habits. If you use sloppy and "non-efficient" fingerings it generally makes playing more difficult. If you learn efficient fingerings then playing is easier.