If you’re interviewing for a specific show and it would be your first time with the theater company, I’d ask a lot of prep week type questions:
-what is the rehearsal room like, is there storage space there
-how soon do rehearsals move to the stage
-what is the director like/have they worked with the company before
-what is the typical tech week schedule for the company
-what is the company philosophy on Previews (good time for script changes vs. perfecting the tech)
- do you have a PA or ASM in rehearsal and what is their background (paid/unpaid/student), how many crew will run the show
-does the SM call from the booth or backstage
-who handles script changes? Will there be a dramturg? Will there be an Assistant Director?
-Is there an SM office/computer/printer/copy machine? Does anyone else use that office as well?
-Who are the other department heads you’ll be working with (is there a TD & ATD on staff? Is there a Costume Shop & Manager, or do designers work on their own? Is there a crew head, or does that fall to the SM? Does the ME run the light board? Is there a resident sound person?)
If you are interviewing for a year-round position, some of the above questions might still be good, but you might want to ask more generally procedural questions. You would also want to ask about benefits, and how requests for time off and sick leave are handled, and who your direct supervisor is.