Do Mormons accept another Christians baptism as valid even though several Christian denominations don't see Mormon baptism as valid?
No. They typically ask new members to be rebaptized. See here: http://mormon.org/faq/purpose-of-baptism
Some do and some don't. It all depends on personal belief.
No, they believe their priesthood is the only one who has the right to baptise.
No, baptism is how you become a member of the church. So baptism from a previous religion wouldn't matter, and since baptism is done by the power of the priesthood other religions baptisms aren't "valid" because they don't have the priesthood.
There s only one valid baptism: Matthew 28:19. But remember its a symbol of repentance and giving up on the sinful life. It doesnt clean people from sin. (John 1)