The shroud is the most scientifically studied artifact in all of history, and there is no evidence, that hasn’t already been debunked, that it is fake.
Regarding hair length:
“ The pictures we have of Jesus with long hair do not derive from any physical description we have of him in the Bible, because there is none. The basic image comes from a long artistic and iconographic tradition—influenced, among other things, by the Shroud of Turin. However, this tradition does not contradict the Bible.
Part of the problem in discussing hair length is how long is long? We know from archeological materials such as Middle Eastern carvings and Egyptian tomb paintings that Jews wore what we would consider today as long hair and beards. Hair reached down to the shoulders on men. Women wore hair down to the waist.
St. Paul was telling Corinthian men that wearing hair down to the waist as women did would be effeminate and contrary to what natural law would suggest, especially considering the physical demands of many first-century male occupations. It is easy for us today to assume the length and cut of a Jewish man’s hair in the first century to be as it is for most men today, but that’s a misconception that can result in our misreading Paul.”
Some thoughts on Hair. We don’t know how long Jesus was in captivity, since there was a lot of arguing among the Jewish elite and an indecisive Roman ruler. Could be enough time for longer hair, no cutting tools allowed. Short hair was easier to keep clean of lice and nits. Women with leisure or servants had time to comb long hair and clean out vermin. Judging from observation in urban areas with Negro population, some young women spend time doing this, even on their young boyfriends. The cutting or arranging part, thankfully not much vermin in our time.