I was wondering if after a priest has been laicized and granted dispensation can he marry in the Catholic church and does he remain a Catholic?
The short answers are yes and yes.
But a more complete answer is that even after being formally and properly laicized, he is still a priest, with all the powers that a priest has. He is simply not permitted to exercise them except in truly extreme circumstances. For example, if he found himself on a doomed aircraft, he could give a general absolution. Or if he came upon a car accident he could hear the confession of a victim in danger of death. In both cases his actions would be both valid and licit.
I bring this up not to confuse the matter, but to clarify it. Once a priest, always a priest. So strictly speaking, there is no such thing as a “former priest”, although we do use that term in colloquial speech.