I've never heard of having to pay to get into a birthday party either strange. As far as presents go, I would get a small gift and keep it in your bag and see what others do. If most people are showing up with a gift, bring it out; if not, keep it in your bag and save for the next bday.
I totally agree with this. I would almost guarantee at least 1/2 of the invitees will bring a present AND pay the admission fee. It as poor etiquette for the birthday boy's mother to put that on the invite in the first place.
My 4 year old would notice that we didn't bring a gift yet others did and he would feel really bad. Of course he'd be happy to swim...but we have a couple of friends with indoor pools so he does that all the time.