I didn't get tickets for an opening night on a Thursday @ 7pm, however, I bought tickets for the same day and exhibition at 5pm. Would I be able to stay in the museum until the event at 7pm starts? Would the staff require me to leave? Thanks!

Yeah, once you are inside, you are there until you leave

Once in, You can be in the museum for as long as you wish until its closing time!

Umm I got the general tickets, and was in and out all day, until they closed.

Once your inside your Ok. Nobody is roaming around enforcing time limits. But you can see everything in the museum in less than 2 hrs so you may be lingering around in the meantime.