Generally warm-up, working techniques and then sparring. On your first day, they'll probably let you sit out sparring (which is good, because you get your ass kicked the firs time you roll).
1. What do you guys tend to do at your gyms?
Yes, but, again, be prepared to get you ass kicked, and don't be bothered by it.
2. Can dudes grapple with girls?
My first time training in an adult setting my training partner was a Pan Am runner up who was about two months away from getting her blue belt. She wiped the floor with me. She's still one of my best training partners.
Yes. Just be a man and suck it up. If you roll with fat, bald guys (who, in my experience, are always the sweatiest) your going to get sweat on.
3. Do you get sweat on a lot while on the ground?
I have no idea what you mean by "gayness factor," but I'm going to just say no. Gang **** should not be a concern on the mat. Focus on not getting your arms broken.
4. Is there a gayness factor? Not trying to be insulting/offensive but are there some typical criteria to follow when im on my back and a dudes on top of me?
It sounds like it will be for you, since you're struggling to get past the concept of grappling, but you get used to it.
5. Is it weird to start, or will I become acquainted with guys being in these positions with me?