Can you show us what you have tried. As a starting hint, remember something is perpendicular if <a,b> = 0 and each line has a direction vector so in order to be perpendicular, both direction vectors must be orthogonal.
In terms of number 2, remember that an intersection is just when one thing equals another. What is the definition of the x-z plane in equation form? How can you make them equal one another and find a solution?
For number 3, you have the area of a triangle using normal high school math (something like 1/2absin(C) where a and b are the lengths and sin(C) is the angle formed between those lines) so |AB| = a and |AC| = b.