Why do you need to have quads? Why do you need to have quads? Is it for animation for when you put bones in and move something around like an arm, or is it something else?

If say a plate with no moving parts or a ball would it still need to all be quads? A ball would move around but it wouldn't move around like say an arm or a face. Let me know if you need more clarification. The asset is to be put in a game.

Also does the quad need to be square shaped or does it just need to have 4 verts?
It doesn't need to be quads.

HOWEVER: many deformation-algorythms and generative modifiers (Subdivision Surfaces) will produce cleaner results if you feed them only quads.

Most gameengines wont work with ngons, as they can be troublesome to deform correctly, so you should use either quads, or triangles.

Also, calculations for quads and triangles are very fast compared to higher polygons or ngons.

About the shape of a quad: a quad is a planar convex 4point-poligon. That means it's flat and no corner is dented in.