In general definitely don't do a deposit. Also in general it's best to be kind of general. haha. Instead of saying, "I'd like you to fuck me doggy," for example. You say, "When I am with guys I love to be fucked doggy." Technically the first is a specific sex act that if you exchange money for, could be technically cosnidered prostitution. In the second you are just saying what you are into sexually with another person. I also always ask, "What do you request for an hour of your time?" Instead of "How much for sex?"
This is why a lot of escorts ask the question, "What are you into?" Instead of "What do you want me to do?"
It's semantics but legally there is a difference there.
But no, I don't think police are on RM and I think you are probably being paranoid.