You could look for the body- but, canonically, the body was given to one of Jesus's followers (Joseph of Arimathea; see Matthew 27:57 and John 19:38 for descriptions of him as a disciple of Jesus), so we have no idea where the body is, besides his claim to have put it in a tomb. Even if he's being honest, there are certainly other ways for the body to have vanished- for example, the Jewish Toledot Yeshu claims that a gardener named Juda stole the body.

All alternative explanations to what happened to Jesus' body really point to the fact that his enemies were unsuccessfully scattering to explain the resurrection away, since they couldn't legitimately counter the claim. Just because there are alternative explanations doesn't mean the original claim of resurrection is false. Of course there would be alternative explanations, since the Jewish leaders had to formulate some type of response. Those explanations didn't work back then and they still fall short today.

We also don't have solid evidence that he ever died- again, according to the Bible, Herod was astonished at how quickly Jesus died, and had a centurion check. That one man's check is the reason it was believed he was dead; it's certainly within the realm of possibility that he was wrong. (Or, for that matter, that the Roman officer didn't feel actually giving a proper medical check, which would involve walking up to and feeling, closely and repeatedly, Jesus's bloody, sweating, dirty body.) (And your prior should possibly favor that- after all, there have been many more verified cases of mistaken death pronouncements than there have been resurrections.

The Romans were not inexperienced executors. They had it down to a science. It would be strange that these experienced executors would suddenly not be able to tell a dead man from a living one. Maybe it was Billy's first day on the job? Also, I should think that Joseph Arimathea, who you mentioned earlier, would have noticed that Jesus was still alive before placing him into a tomb, which was guarded by 2 combat hardened soldiers may I add. The Jewish leaders were not stupid, they were quite meticulous. They knew Jesus had made claims to a resurrection and safe guarded against anything that might mislead the public into believing that he actually resurrected. One of the very things they safe guarded against was those sneaky disciples somehow stealing his body and claiming he resurrected. This explains the guarded tomb with two soldiers.

There were witnesses, of course. Almost all of them were Jesus's disciples, a small band of fanatical followers, some of whom would later demonstrate their willingness to lay down their lives for their faith. (Your claim that he was seen by 500 is flat out non-biblical.

It is not an un-biblical claim because I got it straight out of a passage in the Bible;

1 Corinthian 15:6 - After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep.

Also, most gospels present the resurrection as having been seen by some Roman soldiers, who were then supposedly bribed to claim that the disciples had stolen the body. In other words, there is no reason to trust the witnesses who definitely were there, and all of the ones whose word could potentially be trusted (and who might not have been there) did testify that Jesus wasn't resurrected- because they were supposedly bribed.

Wild speculations. There is no reason to not trust the eye witness accounts of the life, death, burial, and resurrection of Christ.