You still just get 1 free grapple attempt, and the NPC you hit is grappled if your free grapple CMB roll beats the NPC's CMD. The grab special ability does give you +4 to grapple checks though:
"Creatures with the grab special attack receive a +4 bonus on combat maneuver checks made to start and maintain a grapple."
It's a Monster Rule, and i don't know if any options exist that a PC could gain a "grab" ability. If that option(s) do exist for PCs and work like the Monster Rule "grab" ability, then yeah, +4 to grapple maneuvers.
Constrict special attacks have an associated damage that is dealt whenever the person with a constrict ability succeeds on a grapple check (whether it's to begin a grapple, maintain a pin, whatever).
Because as soon as you grapple your target it's grappled. Just because you have two abilities that let you make free grapple checks doesn't mean you get two free grapple checks as a result of one hit. Just like combat reflexes doesn't let you make multiple AoO's off one opportunity.
On the other hand you have vicious stomp and greater trip where you do get two AoOs (also, free action release).
Vicious Stomp and Greater Trip are AoOs that are triggering off of different conditions. That is the reason you get both. Vicious Stomp for when they fall prone (you would get this if they droped prone for other reason or on their own). Greater Trip for actually tripping them.
Take Note: I believe the AoO for Greater Trip happens before they gain the prone condition. Vicious Stomp is taken after they gain the prone condition. This will make a difference with +hit modifiers.
correct on all accounts, slacker.