Does encryption using PRP mean indistinguishable encryption against an eavesdropper?
The PRP encryption scheme is secure in your security definition, but this security is very weak. It only achieves "one-time security" and is also weaker than perfect secrecy, i.e., the adversary's advantage is not exactly 1/2.

I think the security can be stronger (but still cannot be IND-CPA for instance). With PRP security, we can view $F_k$ (and hence $Enc_k,Dec_k$) as a real random permutation $f$ (except for a negligible PRP security advantage). Then, even if the adversary knows $p$ message-ciphertext pairs, it still cannot distinguish $m_0,m_1$ if they do not belong to the known $p$ messages.