Paul encountered Jesus Christ in a vision on the road to Damascus. For him this encounter was very real and life changing. I suspect that as Paul got to know his new Lord, he would have wanted to meet as many people as possible who had actually known, or encountered, Jesus face to face. His realisation that everything about his faith in Jesus Christ was dependent on the resurrection being real, would have made him particularly interested in those who had met him, in the flesh, after his resurrection. This was life and death for him. If it hadn’t happened, why was he puting up with stonings, imprisonments, 49 lashes, ship-wrecks, intense opposition from his former colleagues and friends, and finally death?
You’ll have to get “evidence” on the authorship of the Gospels from someone more competent than me. Though I have never had a reason to doubt that Matthew, Mark Luke and John actually wrote the gospels given their names, I have been more interested in evidence that what they wrote is true, if only as their perspectives of what they saw, heard from fellow followers and Apostles. Luke, as a Greek, strikes me as particularly trust-worthy, because he writes many things in a literary format that is/was unique to the Jewish writers. He could not have made these stories up himself, so he must have got them from others, probably cross-checked and confirmed, and presented them in the format he received them. (See Kenneth Bailey, Jesus through Middle Eastern Eyes for elaboration, description, and many examples.)
With regard to the resurrection, the more I read the stories of Easter morning, the more believable they get - they reveal so much about human nature, that I recognise in myself and others, even today. The strongest point (for me) is that at first, NONE OF THEM BELIEVED IT! It was unbelievable if true. People simply don’t come back to life from a crucifixion death. Not three days later! We are unfair to Thomas and call him the Doubter, as if he was the only sceptic, but he wasn’t! NONE of them believed it! The irony of that morning was that the people who took the event most seriously were the guards and the chief priests. They took it so seriously that the Priests bought the silence of the guards and started a campaign of fake news - “the disciples have stolen the body!” (Do we recognise a cover-up in high places?) Why, in that case was Mary asking (even after meeting the angels) the gardener if he knew “where they have taken the body?” It wasn’t until he spoke her name, and she recognised his voice, that it dawned on her that it was true - and that he repeated what the angel had said.
As to numbers, you will find quite a few mentions of significant numbers of followers of Jesus in the Gospels. We often think there were only 12, but this isn’t accurate - these were only the apostles, a special group of disciples. Jesus sent out 70 or 72 to practice preaching and healing in rural villages. There were about 120 followers in the upper room on pentecost. There are a lot of named followers too - Mary, Martha, Lazarus, Joseph of Aramathea, (probably Nicodemus), Mary Magdalene, the two on the road to Emmaus, and reference to a lot of women who followed Jesus and supported him. Probably a large number of these individuals were among the 500 Paul refers to.
Another thing: After Jesus was captured and crucified, his followers were petrified that the authorities would turn on them, to stamp out all remnants of this blasphemous teaching. They admitted their fear in the stories; there is no white washing of the apostles’ or disciples’ behaviour or feelings. (Saul was later part of the attempt in fact.) And yet not long after, their fear had changed to boldness that amounted to “turning the world upside down.” And it wasn’t a temporary thing. This movement fundamentally changed the nature of the Roman Empire’s society over the next 3 centuries.