Is it True that FP and Finn Break up?

Yes, they broke up in Frost & Fire. Finn tried to get back to Princess Bubblegum in the following episode, Too Old, but he rejected him because she was focusing on some লেবু child (I forgot his name). At the end of Too Old, Finn ব্যক্ত he would try to fix things up with Flame.
In Earth & Water, FP becomes Flame Queen. When Finn asked if they were still going out, she ব্যক্ত no but they could still be good বন্ধু if he was completely honest to her.

Yup, but in the Earth and আগুন special they become বন্ধু again but not boyfriend and girlfriend.

Ya, but like with Tony and Jessie on Jessie, I don't feel angry bout their breakup. I feel at peace with it.

Not really, in that episode FP ব্যক্ত she needed some time alone but in the following episodes she ব্যক্ত they can still be বন্ধু and she took over as her her father

no