If player one has built a road system through intersection A. Is it within the rules for player B to build a road system that passes through intersection A from the perpendicular direction? Or is that illegal since player A has already built roads passing through that intersection?
What you say is not possible, as there are only 3 different ways that a road could go into an intersection (and in some places just 2, so perpendicularity is not possible). However, it is technically legal for someone to build a road into an intersection where another player already has two roads going through. (Other than the purpose of blocking a player's route however, this is not usually a beneficial move for the player taking it.) In the below example, the green player could make a road going into the red player's intersection legally. (Sorry for the green, I know its not a Catan color, but it was the only color arrow I had.)
It is also legal for a player to insert two roads, effectively blocking another player's route into an intersection in which he has only one road. In Example 2 (below), the green player built two roads to cut off the red's road at the water-ore-desert hex.