Okay, Jesus never said he would rise AFTER three days. He'd rise ON the third day. He dies on Friday (day one) which'd make SUnday the third. Although there is a good case for Jesus having indeed died on a THursday. THis has to do with a complicated situation of an extra sabbath because of a special year or so. Forgot exactly how that worked. It doesn't matter really. And there is evidence that Jesus lived AND died. Roman sources reported the crucifixion.
Ah yes, the mysterious shroud. Still, however weird that is, it's not very definate proof yet. I mean, it's quite clear the carbon dating on that was very badly done.... but still.
There is however, a pretty genuine fragment of the sign that hung over Jesus's head in the cross. Only the right side remains, but since the Hebrew, Greek and Latin is written from right to left (depsite the fact that noirmally Latin and Greek are written from left to write and Hebrew is written from right to left) scholars seem to tend to accept this as genuine.