P4P is basically about very basic human needs. The hon shimei fee lets providers know that you appreciate their service, and that reflects in the way they treat you. (To be clear: I’m not talking about extra services or anything, just the quality.)
Again, you get a guaranteed provider you want. A bad provider can make you feel worse after a session, and for people that might go rarely, they'd prefer to pay a little more to deter that risk. The other thing is providers get a bonus for repeat customers.
Personally, I'm the type fine with trying out new providers that offer even more of a discount even when picked. The reviews I make then are useful for others to make a safer choice.
As for AF, it's not a euphemism. It's for anal sex. Anything discussed beyond that is between you and the provider. No discussion of that part beyond the AF is permitted on the forum.
In japan there is no tipping. So honshimei is one way to reward the girl for doing good job. Repeating is sign of good job and girls can earn extra from repeaters.