1. The few sessions I've been to we did some stretching, then some warm up drills like taking shots, hip stretching stuff, running, etc. Like Wakkudb said, your instructor will show you a guard pass, sweep, subbmission, etc, and you'll drill with a partner. Finding a partner isn't hard, but it's better if you scope out someone around your size before you get started and approach them. After drilling you will go live. It's always very fun for me.
2. I never grappled with women. That seems like it would be very awkward. Women were never in my class. I highly doubt you will.
3. Yes, if you're worried about sweat then you probably shouldn't get into grappling or MMA or any sport with physical exertion.
4. I guess if you have never done a combat sport it may be wierd to have a man mounting you, but to me it's not wierd at all. You won't be worried about how gay you look when your joints and/or bones/ligaments may be in danger of snapping.
5. It's really not wierd at the beginning. You just find a partner and go. If you don't know what you're doing then I'm sure your partner will and they can help you out. Everyone I've grappled with has been fine.
And on a side note I've never kissed a guy. What the hell xeberus...lol.