Perseus, welcome to the forum.
I think it will be suggested that you miter the corners, which will take care of the alignment question.
I see that you have marked with a pencil where one piece intersects with the other. If you want to join those two in that fashion without using a full miter, then you would need to try and cope that joint.
I think the miter will be much easier.
One of the mods might ask that you fill out your profile so we know your first name. We don't bite here, and yes, I think you are in the right place.