Is this reasonable? Or is it unfounded jealousy?

My girlfriend has started college a few months ago. In general I have no problem with her acting, in fact, I've encouraged her to go on, and did a lot to help her get into acting school in the first place.
However, things are starting to get problematic for us. We live in different countries, and I come to visit her for 3 months at a time, and then leave until I am able to come back.
When I am not there, she has get-togethers and parties at our apartment, where all sorts people from her university come. That in itself is ok with me, but it has come to my attention they do all sorts of stuff like playing spin the bottle, strip teases, getting naked, etc...

And a lot of the times (or most) people end up staying over the for the night. Since it's a small place, people end up sleeping together on spare beds, couches, and even on our bed. On occasion other couples have had sex in our bed in the bedroom.
What really bothers me is that she sometimes sleeps in the same bed with other guys, who I know like her, and have been getting drunk at the party. There is no confirmation or evidence that she has had sex with them, and she swears this is all normal. She says I'm being weird by having a problem about her sharing a bed with other men.
Is this supposed to be normal? What do you all think, is it OK for people of the opposite sex to sleep in the same bed after a debacherous party normal? Am I being unreasonable by asking her not to do so?

Another issue we are having is that she insists in wanting me to be OK with her being naked in front of other people. She says that in acting class they don't have a place to change clothes, so they all have to change in front of each other. While I am not thrilled by the idea of other horny guys seeing my girlfriend in underwear, that is no where near as bad a fully nude. She says that she wants to do acting where she will be naked on stage in front of everyone we know. As well, she wants to do sex and kissing scenes, and says I need to be ok with that.
While I am ok with her doing these things if she ever has a serious role professionally, I feel apprehensive about her both being naked with, doing sex/kissing scenes with her classmates. She spends an awful lot of time with them, on average 10-12 hours every day, including after classes and on weekends. It's not like in professional acting where people doing a love scene meet only on the set, and then return to their normal lives. I simply don't like the idea of her being naked with and romantic with these people. I am being unreasonable here?

I know these are two very separate issues, and I'd appreciate an answer for both. I put them together in order to give a better perspective on what I'm going through. She has cheated on me with two other guys in the past, which was a traumatically painful experience for me. Last time was last July, and since them I've found it very hard to trust her or be OK with all these things she wants to do. I really love her, and have been with her 2.5 years now. I want to be with her for life, but I don't know if I will be able to cope with all these jealousies that she triggers in me.

Please help