Additional things I always wish I ask upfront --
Under the umbrella of 'approval' - what is the chain of command for personal day requests, vacation time requests, and MRE?
I find in some instances the general manager is also wearing the company manager hat so I ask questions of that nature if that is appropriate, for example birthdays, show anniversaries, announcements, etc.
Petty cash protocol, reports or logs they may prefer in their office. (I've worked where PM is in charge of petty cash, but often on off-bway shows the GM team deals with it directly)
I usually ask what their schedule will be like during rehearsals/tech/performances, as in when are their office hours, if they prefer calls to email, and what is usually their schedule during performances. May come off really nosy, but it's nice to know how and when they are available especially if they are the micro-managing type. It really helps cement a protocol and schedule during performances if there is a designated time that they stop by the booth or green room so we can check in with each other and say hello.
Some things may not be applicable in your situation but these are just a few that I always mean to ask --