1. You can, but only for certain actions. I assume you want to make the grapple checks to do damage or pin your opponent, both of which are stated to take the place of an attack.
1b. If you are not already grappling and wish to initiate a grapple, you can make the attempt as your AoO (including having to start with possibly provoking an AoO if you don't have Improved Grapple or the like, then needing to make the touch attack). If you are already in a grapple, however, you have no threatened area and therefore are unable to make AoOs in the first place.
2. It just takes an attack to pin, so if your BAB is high enough, you can have extra attacks available to use.
3. Speech is not required to use a breath weapon, and being pinned does not prevent you from breathing or using SUs, so yes, you can use a breath weapon while pinned. However, if you try to breathe on the foe grappling you, your breath weapon will also hit you, as you are sharing his space, unless your foe takes up more squares than you do.