I'm from NJ.

Suppose I'm at a MP and the girl is giving me a nude massage, but nothing has happened sexually, not even HJ. Legally, am I safe? I would think so.

Another question--Suppose I have sex with a MP girl but I don't give her any money.. she happens to like me. Is that illegal?

You may be on the right side of a fine line with your questions.  I'm no lawyer so I can't say for sure, but here's how it plays in the real world if you ask me:

Prosecutor: He entered an establishment known to provide sexual favors for money.  He paid $, took off his clothes and the woman had sexual intercourse with him.

Defendant: But Your Honor, she liked me!

Judge: GUILTY, *gavel bang*, next case

Prosecuter: Your honor Mr jones was founf naked on a massage table along with Ms Smith who was also naked. It's the states assertion that Mr Jone had agreed to pay Ms Smith for sex acts. Money had been exchanged.

Defendant: but judge all I wanted was a massage.

Judge: Guilty (gavel bang) Oh, Mr Jones I see you have a previous conviction and this is a violation of your probation.
90 days and $1000.00 fine. Have a nice day