Can Luigi get out of being convicted if he runs for election as a member of the house of representatives?

No, he needed to get elected before allegedly committing the crime and then it would have been an act of government

He should try being overwhelmingly wealthy. That usually works.

It's more likely he's held indefinitely with his right suspended due to his "terrorism" charges imo

Is his family wealthy enough?

Pretty sure you need enough monew to throw around in addition to running.