Do I have to pay for a Peeranha Post?

Peeranha protocol runs on Polygon blockchain. Polygon blockchain takes fee to send a transaction. However, Peeranha web interface will subsidize transaction fee if MATIC balance in your wallet in 0. A meta transaction will be posted by Peeranha transaction relayer in that case.

Other than that it is free to post on Peeranha. The protocol itself doesn't collect any fees.

Answer, yes. You have to pay to post.