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Thanks, I'm started to get a clearer picture of how this works. So this part of the grab rules:

If the creature does not constrict, each grapple combat maneuver check it succeeds at during successive rounds automatically deals the damage indicated for the attack that established the hold.

Isn't describing extra damage a creature gets to do on every grapple check after the turn it starts the grapple, but rather a restriction that when it does make a grapple check to maintain a grapple and chooses to do damage to the target rather than move or pin, that damage has to be from the natural weapon it used when it started the grapple? While Constrict is additional damage on every successful grapple check in addition to it's normal effects?

So if I understand correctly:

Creature with Grab but not Constrict
Turn 1 (Attacker's Turn): Creature makes a successful natural weapon attack against a PC and deals damage, and then gets to make an immediate grapple check as free action without provoking AoO to start a grapple. On a success, both creature and PC are now grappled, with the creature controlling the grapple. Creature deals no additional damage for having successfully established the grapple.
Turn 2 (Defender's Turn): PC makes a grapple check to attempt to break free but fails. Creature deals no additional damage at this stage.
Turn 3 (Attacker's Turn): Creature makes a grapple check at +5 to maintain the grapple. On a success, the creature may do one of the following:
-Deal damage with the natural weapon they used to start the grapple
-Move themself and the grappled PC up to half the creatures movement, dealing no damage from the grapple this turn.
-Pin the grappled PC, dealing no damage from the grapple this turn.

Creature with both Grab and Constrict
Turn 1 (Attacker's Turn): Creature makes a successful natural weapon attack against a PC and deals damage, and then gets to make an immediate grapple check as free action without provoking AoO to start a grapple. On a success, both creature and PC are now grappled, with the creature controlling the grapple. Creature deals constrict damage to the PC for succeeding on the check to start the grapple.
Turn 2 (Defender's Turn): PC makes a grapple check to attempt to break free but fails. Creature deals no additional damage at this stage.
Turn 3 (Attacker's Turn): Creature makes a grapple check at +5 to maintain the grapple. On a success, the creature may do one of the following:
-Deal damage with any natural or light/one-handed weapon they possess to the grappled PC, plus deal constrict damage on top of that.
-Move themself and the grappled PC up to half the creatures movement, plus deal constrict damage.
-Pin the grappled PC, plus deal constrict damage.

I can't seem to find a clear and consistent answer for how damage from the Grab and Constrict abilities work.

The creature has the option to conduct the grapple normally, or simply use the part of its body it used in the grab to hold the opponent. If it chooses to do the latter, it takes a –20 penalty on its CMB check to make and maintain the grapple, but does not gain the grappled condition itself. A successful hold does not deal any extra damage unless the creature also has the constrict special attack. If the creature does not constrict, each successful grapple check it makes during successive rounds automatically deals the damage indicated for the attack that established the hold. Otherwise, it deals constriction damage as well (the amount is given in the creature’s descriptive text).

I believe, but am not certain, that the parts about automatically dealing damage on successful grapple check are not contingent on taking the -20 penalty option, and that the only benefit of that option is not gaining the grappled condition yourself. What I am less clear on is, if a monster has both Grab and Constrict, and chooses to use constrict on a grappled opponent, is the constrict damage is addition to automatic damage for the attack that established the hold from grab (in which case why the If/Otherwise statement?), or instead of that grab damage (in which case why do the rules say it deals constriction damage "as well" rather than "instead"?)

Also, does the damage from Grab and/or Constrict replace the normal rules for dealing damage on a successful grapple check, or can a monster do natural attack damage using the damage option, in addition to Grab and/or Constrict damage?

Once you are grappling an opponent, a successful check allows you to continue grappling the foe, and also allows you to perform one of the following actions (as part of the standard action spent to maintain the grapple

Damage

You can inflict damage to your target equal to your unarmed strike, a natural attack, or an attack made with armor spikes or a light or one-handed weapon. This damage can be either lethal or nonlethal.

And is my understanding of RAW correct that Constrict allows you to deal constrict damage in addition to making other action you would normally get to make for succeeding a grapple check such as moving the grapple or pinning your opponent?

A creature with this special attack can crush an opponent, dealing bludgeoning damage, when it makes a successful grapple check (in addition to any other effects caused by a successful check, including additional damage). The amount of damage is given in the creature’s entry and is typically equal to the amount of damage caused by the creature’s melee attack.

Also, is there a grapple flowchart anywhere that includes Grab and Constrict damage?