Wasn't Muhammad born in the year 570 AD, while Jesus was born in 4 BC? Yeah not really contemporaries o_O. Unless we're going to stretch the definition of "contemporaries" to allow a Galileo vs. Hubble telescope debate or something
You lost me when you started with the prophecies. One of the reasons Jews don't believe that Jesus was the Messiah is because they weren't told there would be a second coming. Even if Jesus didn't die he didn't fulfill the prophecy.
This website has a pretty good list of the prophecies we use to justify the first coming. I know, I know, that website doesn't exactly have the best layout, but at a glance it seems to have everything I was looking for. True, I couldn't find an exact prophecy that said Jesus would come to earth twice, but when you look at all the prophecies (I'm a bit annoyed how this website says there's about 60 and it only lists 45, this isn't helping my case much...) you start to see a contradiction. On one hand, the Messiah is going to be betrayed and killed, but on the other, he's going to save Israel. With that in mind, and along with the accounts of the Gospels where Jesus pretty much explains how role at the time, we Christians believe in a first and second coming.
I'll just rest my case here. I doubt I've convinced anybody but oh well, that's what we believe, and in a round about way, why Jesus told his disciples not to tell anyone he was the Messiah (at least not tell anyone at the time).