Maya help teaches that when final gather is incorporated, mental ray will not use photons, but samples the semi-hemispherical area above points in the scene to calculate the illumination.
Ambient Occlusion refers to the darker aresas of the object, typically creases, cracks and crevices. It is caused by indirect lights inability to bounce around and illuminate areas that are blocked by a nearby object that absorbs the light rays. It helps add realism to the scene with shadows.
For the area light source i believe it is just the light you can pick in maya lights. The help menu states to use them to simulate the rectangular reflections of windows on surfaces.
Basically rendering with global illumination is the same as above. It does make you render time longer so make sure you need it and cannot cause that effect any other way.
Render layers are good because you can assign any object to multiple layers with a different material on each layer. Which lets you create multiple images for each frame.
From the render layer editor, you can create, manage, and delete layers, layer blends, and layer overries. You can also create render pass contribution maps for your render layers.
The master layer contains all the objects and materials in the scene. There are two types of overrides for attributes, per layer and per object. Per layer overrides change attributes, characteristics, or materia assignments that affect the entire layer. Per object overrides change the value of an attribute or material assignment on an object in a specific layer on which overrides exist.
A PSD file is created during a render with each layer in each layer in your scene as a separate layer in this PSD file and with all blending modes specified as they were specified in the Maya file.