The priest that Brian 'brought back from the dead' wasn't really dead to begin with. Brian used one of those electric shock thingies to bring him back, but the people there didn't have anything like that so they called it witchcraft.
Arthur's father was a doctor, and he tried to make Arthur one as well before he left home for Camelot.
After Arthur was shot into the sky in the life pod at the end of HNOC he traveled for a very long time, by the time his life pod landed on a new planet he had spent so long in stasis that he didn't really remember who he was before.
He remembered being a doctor, and he remembered that Brian was a name, so he became 'Brian the doctor'. Fort Galfridian had better medicine and technology than the planet he landed on, so he was hailed a miracle worker as a doctor.
Then he 'revived' a priest, and was shot into the sky for witchcraft. that's how he became 'Drumbot Brian'
He still doesn't remember Camelot, but that's why he tried so hard to save everyone, that's why he became Merlin. It's also why he failed, there was never any chance of success to begin with.
History repeats itself and time is a loop.
Jonny as One-Eyed Jack was a pretty good similar idea.