Can A DemiGod Become A God And How

yeah a god can grant a demigod immortality, but only if they're a hero and did something that really impressed the gods. the how part, im not sure :p

If a demigod performs a great feat and the gods offer it to him/her, the demigod can be granted immortality, but it only happens once in a great while.

It depends on how awesome the Demigod is, so Percy Jackson qualifies.

Yes. A good example of this is in the case of Jesus. His mother was a mortal and his father was a God. In order for Jesus to become a God, he needed the blessing of a God and his mortal half to die. Only then, He could be reborn and become a God.