I for one believe this is the shroud that covered Jesus, I see no reason not to, and there is nothing on that shroud to prove it is false.
It was not painted, it is a visual of a man who was crucified. Only a resurrection energy could have caused that imprint to happen, that's Jesus.
I believe his mother saved that shroud, as any grieving mother would and it was passed down to her family.
There is no reason to believe that GOD would care if we knew what he looked like in the human. None that I can see.
Do believers need this to have the faith in our Lord Jesus? NO.
Yes and no :-) One critical belief of Christianity is that Christ was a corporeal, flesh and blood man. One quality and characteristic of all humans is "appearance," and consequently, this was also a quality of Christ...just as having ten finger, two eyes, a nose etc. Now, Christianity isn't contingent on whether Christ was tall, short, handsome, homely, bearded, clean shaven, etc...those things don't matter, but what does matter is that He did have a human appearance.
Christians of vastly different cultures and races have portrayed Christ in a manner that has made it easier perhaps for them to form an identity and more personal relationship with Him, and in and of itself, I don't see anything wrong with that. Having said that, He did have an earthly, human persona and image, and I think any person with a burning desire to know Christ as fully, intimately and personally as possible can help but speculate about and want to know what he truly looked like...
Just my two cents...