I actually had to write a program that would automatically generate excel spreadsheets and graphs programmatically and it took forever to track down the documentation needed to do this. Although that doesn't sound like what you are doing it will get you in the right direction.
The above solutions are the common ones used. If your objects are moving extremely fast you might want to consider casting a ray from the 4 corners of your bounding box from the old position to the corresponding corner in the new position. The collision ray with the smallest magnitude (if any) is where you will need to resolve your collision and impart any forces on the colliding objects.
Actually your suggestion seems quite sound. Using an AAB that completely encompasses your AI's FOV could be done for a quick check to see if the player could be in the enemy AI's FOV. Then perform a raycast from the enemy to the player to determine if the player is actually in the line of sight of the enemy. Raycasting can be done using DDA. Which is pretty quick if you are only casting one ray.
I am not sure about your layer concept. If you mean the upper halfof the screen is a different layer vs the lower half. Then the same grid or matrix you use for collision detection is the same one you cast your ray into.