… For example: Can one play the Time Car v1 when he does not have some form of Plutonium?

A: No. When you use Rewind, it becomes the same as if the card you got from the discard pile had been played from your hand. So playing the Time Car v1 via Rewind would be exactly the same as if you played it normally. If you do so when you don’t have the needed Plutonium on the table, nothing happens.