I agree with @Jeff158 - update your profile photo to one of you. Just as we hosts like to see a photo of our prospective guests rather than, say, a sunset, they like to see a photo of us.
To answer your questions:
No one gets the deposit. It is just a safety net if the guest causes any damage. I believe the safety net has quite a few holes in it, but it's probably worth doing anyway.
Airbnb charges 3-20% service fee depending on a number of factors. I'm not sure what you'll be charged but you'll find out after your first booking.
You are normally paid sometime within the first 24 hours after a guest checks in.
Yes, you can do a minimum stay of 3 nights - go to your listing > Availability > Trip Length. Here you can set your minimum and maximum nights.
How much to charge - you need to look at what other hosts are charging for similar listings in your area as well as your expenses, taxes, etc.
Parties: under house rules, you can tick where it says 'No parties or events'. You might consider installing security cameras outside as well.
Include any taxes you have to pay in your nightly rate.
@Amanda1108 I'd suggest that you read everything available for hosts in the Help section of the Airbnb site. You'll get a lot of answers there and if anything is unclear or you can't find the answer there, just ask away here.
Airbnb charges 3% of the listing price to hosts for each booking. Fees to guests are anywhere from about 10-20%. We don't know the formula Airbnb uses to calculate the guest fee- it's a mystery 🙂