Wasn’t necessary. He lived and died under the Law.
Baptism (Spiritual death, burial and resurrection) became necessary after the physical death, burial and resurrection of our Lord. At Pentecost.
That makes no sense at all. If he died under the law then he would go to hell not be with Jesus in paradise - he admitted he was guilty of the crime for which he was being executed and deserved to die. His repentence and acknowledgement of Jesus for who he was is what obviously got him into paradise. He was saved under the New Covenant which Jesus had instituted the night before.