Does Pax Romana forbids belief and/or love of God?

The Pax Romana wasn’t a law. It’s more a nickname for the relative peace during the first couple of centuries of the Roman Empire. Open Christian worship was regularly persecuted during this time starting in 64 AD after Nero blamed Christians for that year's infamous fire in Rome.

................no.

The Pax Romana was the 'Roman peace' of the ancient Roman empire. Meaning for a time there were no all out wars because the empire had already taken over just about everything and so could suppress them. As for religion the Pax Romana was tolerant of all 'pagan' religions but not Christianity or the Christian love of God, or it's beliefs, it was illegal, treason and carried the death sentence. The Pax Romana was also intolerant of the Jewish religion but did not usually outlaw it.

You mean DID it forbiD belief in God. No.