Christians claim Jesus rose from the dead; why should we care whether it's true or not?

It's often claimed that Jesus' followers borrowed existing pagan beliefs about resurrection. Is that true?

How can we know that Jesus really did die on the cross?

What should we make of claims that differences in the Gospel accounts mean they can't be trusted?

Are claims that Jesus rose from the dead simply legends that were made up hundreds of years after he died?

Is it possible that the accounts of the resurrection are simply the result of hallucinations brought on by grief?