About the hair/braid. Yes. The Nazarite sect (not to do with Nazareth) wore their hair long - braid down the back.
Jesus's blood brother, James the Just, was also a Nazarite - and he led the Jerusalem church after the Cruxifiction.
You no doubt know that artists in Medieval times painted secret 'messages' in their paintings - things they dared not claim aloud.
In the iconic painting below, Jesus stands with the words "I am the Light". On his right is James the Just with the scroll signifying power. Jesus' hand, signifying blessing is also turned toward James, not outward toward the viewer. On the left is a sour faced Peter scowling across at James. Peter is identified by the symbols of the Roman Church. It was James, not Peter, who led the followers - until he was killed in 62AD, Peter and John were James' two counselors. (It amazes me that people don't understand this as it's plainly written in the Bible.)
The artist is identifying Jesus and James as brothers in their dress - the same colors. The faces are the same - if the James face were turned straight, it would be the same as Jesus.
Note the hair...pulled back and on James you can see that it goes into a braid. (As you probably know, the Nazarites were a sect of the Essenes headquartered at Mt Carmel. Unlike the Qumran sect, the Nazarites were allowed to marry.)