These answers are based on Chicago Unifieds:
Do schools promote that they will be available for walk-ins?
Yes, they put up displays in the lobbies of each floor where auditions are held, put notices on the bulletin boards in the lobbies, put flyers out on the lobby tables, etc. They will also sometimes put the notice on the wall or table outside their audition room. If you “walk the floors” you will find lots of walk-in notices.
What is the process of a walk-in if you haven’t applied to the school?
Schools that do walk-ins generally don’t expect you to have applied to the school. They usually will recommend during your audition that you apply to the school as soon as possible to be considered.
Do schools do walk-ins for musical theater AND acting?
Some do both, some do only one type of audition.
Walk-in slots can fill up quite fast, so it pays to “walk the floors” first thing each morning and sometime after lunch (notices seemed to go up at fairly random intervals between Sunday morning and Tuesday afternoon) and sign up quickly if you are interested.