Q: When was the first picture/painting done of Jesus, by who, and who was the model?
A: Your question - "When was the first picture/painting done of Jesus, by who, and who was the model?" is an interesting one. I wish I had the answer but, unfortunately, I don't think anyone can know for sure.
I think that you are asking about the earliest known portrait of Jesus. I have done some searching in books and on the internet about the topic. The earliest portrait that we know about was probably painted some 1, 700 years ago, during the 3rd or 4th century AD. My guess is that it was painted in Byzantium, (now Istanbul) which was one of the centers of early Christianity. Of course, that image of Jesus would not be a real portrait, as 200-300 years would have passed since He lived on earth. We also could not be sure that a human model was used to create the image. Portraits done during that time were often stylized paintings or mosaics called icons, which didn't try to capture a real likeness of Jesus, but instead were created to emphasize certain beliefs held by different branches of Christianity.
That's the best I can do to answer your question. If you want to learn more, I'd suggest a trip to your library or anywhere you can find books on the history of religious art. I would also be happy to recommend some books to you on this topic.
I'm personally grateful for your question because it led me to imagine who might have drawn the very first picture of Jesus. Of course, that picture would not exist today, because materials used to write or draw upon during that time were not only scarce but highly perishable. And most people would not have access to them, especially the poor and unfortunate to whom he ministered. Also, the Jews who knew Jesus so well were forbidden by law from making images.
Maybe the artist was a local craftsman who was impressed by Jesus' gracious character as He visited with people in his neighborhood. Or maybe she was a quiet follower of Jesus who wanted to remember his kindly face, healing words, and understanding ways (we need to remember how restricted a women was in that society, and how daring the women were who followed Jesus). See The Women Who Followed Jesus Or maybe the first portrait was painted just after his death, created by someone who tried to remember what he looked like, or from the memories of those who knew him. In The Urantia Book we find many stories and descriptions of Jesus that help us understand why people were so attracted to him. I especially love the Section titled, As Jesus Passed By
Personally, I like to imagine that a small child was the first to capture Jesus' likeness, using a stick to draw in the sand or dirt near the family home. Maybe this child was playing with the other children when Jesus appeared, sat down under a nearby tree, and started telling a story. We read that Jesus loved the little children, and that they loved him in return. Perhaps this little child discovered a new experience of love and trust when she rested in Jesus' arms or when he listened, spellbound, to his story. Drawing a picture of the Master would be a natural way to express the childlike joy of being in His presence.
Thank you again for your question. I hope that this has been helpful. It certainly was enjoyable to think about!