This is the answers I came up with by looking at all the answers and the DnDFAQ. I only have 2 doubts, critical hits and power attack, but you'll see this below.
IMPROVED GRAB:
> Imagine this creature for my example : Medium-size, Str 10, BAB +8, 1
> Slam +8 melee (1d6), Improved Grab (Slam), Constrict 1d8
>
> The creature hits with its slam attack, causes damage (1d6) and
> attempts the grapple check immediately.
> -Is the grapple check at +8 or at +3 (since it's a second attack in
> the same round) ? [I would use the +8]
OK for +8. This is the right one.
The grapple check on Improved Grab would be at the same BAB or attack roll modifier as the initial attack, so +8 for the first try or +3 for the second. And it's made at +8, since it is part of the first attack.
> If the grapple checks succeeds, the hold is made, and the creature can
> constrict (1d8).
>
> Next round, if the target does not escape the hold:
> If it can make 2 grapple checks to damage its target, as per its BAB
> of +8/+3, it would have two grapple checks (one at +8 and the other
> at +3). So, if both succeed, the target would receive damage twice
> for the slam and twice for the constrict (1d6+1d8+1d6+1d8).
That's the way it is done, as per the DnDFAQ.
"If the creature begins its turn with an opponent in its grasp, the creature can just hold on or it can attempt another grappling check. If it elects to grapple again and it succeeds, the natural weapon the attacker used in the improved grab inflicts normal damage on the opponent. If the attacker also has the constriction ability, it inflicts constriction damage in addition to natural weapon damage. "
Also, as per the grapple rules and DndFAQ:
"You can make one grapple check for every attack your BAB normally allows. The number of weapons you use doesn't affect the number of grapple checks you can make."
So, it the creature with Improved Grab had 4 attacks from BaB (+20/+15/+10/+5), it could initiate four grapple checks, doing Slam AND Constrict damage with each. Without improved grab it would be 4 unarmed strike (subdual, based on size) and 4 Constrict. Constrict is a very dangerous ability.
> -So, can it make more than one grapple check to damage the creature
> with its slam attack AND constrict?
Yes. As per the answers given above. Because the constrict damage applies with any won grapple check that you use to do damage.
As stated above, if the victim is grappled, all the creature must do is make another successful grapple check to cause constriction damage. The creature can make as many grapple checks as it has attacks (+8/+3 BAB in this case).
> GRAPPLE CHECK:
> It's an opposed roll, but also a kind of attack roll.
> -Is a 20 an automatric hit?
Yes, a 20 is an automatic hit, and a 1 an automatic failure for the attacker only. The defender only sets the DC for the attacker (see below).
As per the DnDFAQ, the grapple check is an "opposed attack roll".
Also from the DndFAQ:
"For the attacker (that is, the character trying ro disarm a foe or accomplish something with a grapple check) a natural 1 fails and a natural 20 succeeds, no matter what the defender rolls. Although the defender's roll is called an "opposed attack roll," the defender is really just setting the DC for the attacker: 1s and 20s aren't special for the defender. Just apply the defender's modifiers to set the DC for the attacker. If both the attacker and the defender roll a 1, the attacker fails. If both the attacker and the defender roll a 20, the attacker succeeds. Note that you cannot get a hold on a foe two or more sizes larger than you (see page 137 in the Player 's Handhook).
…All of the foregoing assumes that you are indeed making an opposed attack roll, which is subject to automatic success or failure. Checks are not subject to automatic success or failure. For example, if you are making an opposed check (as you would when making a Hide check opposed by a foe's Spot check) a roll of 1 or 20 has no special significance.
> -Can you have a critical hit with a grapple check? (If yes, would you
> double the Slam AND Constrict damage?)
As per PH p123:
"When you make an attack roll and get a natural 20 (the d20 shows 20), you hit regardless of your target's AC and you scored a threat."
So, from the DnDFAQ, a grapple check is an "opposed attack roll" that hits redardless of the target's DC. It's also an unarmed attack and an unarmed attack can score a critical hit.
So I would go with this answer if everyone agrees.
YES, a grapple check can score a critical hit, so what!
[I'll take this answer until the Sage answers me]
> -Can you use Power Attack on a grapple check?
As above, since it's an "opposed attack roll" :
YES. It lowers your grapple check as it lowers the attack roll so it gives a better change to the defender to oppose the attacker.
Also, if Power Attack can be used against inanimate doors, it should be usable
in a Grapple as well.
Since it's a feat, all creatures with Power Attack, even without Improved Grab (or Snatch)
can use it while grappling.
> Since the maximum size for the target of an Improved Grab is one size
> smaller than the creature, the Medium-size creature above can only
> Improved Grab Small creatures.
Correct.
> For the normal Grapple, the size of the target is one size bigger.
> So, it could grapple up to Large creatures.
>
> So, the Medium-size creature could make a Grapple if it wanted to
> Constrict a Large enemy. The Improved Grab would then be useless. If
> it touches the target (+8) and the AaO fails (as per the normal
> grapple rules) it has grabbed the target. Now it can automatically
> make an opposed grapple check (+8) to hold the target, causing it 1d3
> points of subdual damage (as per its size) AND constrict (1d8).
This is not correct, the Improved Grab is not useless.
The creature can make normal grapple checks to grab bigger creatures than with an Improved Grab. But it suffers an AaO, if the AaO hits the grab is automatically failed, it moves in the square of its target and can suffer AaO because it moved, etc…
It could then make 2 grapple checks as per its BAB (+8/+3). If it grabs and causes damage, it makes Slam damage AND Constrict damage.
Also, Constrict does not replace the damage from a grapple, it adds to it.
As per the DndFAQ:
"Creatures with the improved grab special attack can use their natural weapons in a grapple."
"If the creature begins its turn with an opponent in its grasp, the creature can just hold on or it can attempt another grappling check. If it elects to grapple again and it succeeds, the natural weapon the attacker used in the improved grab inflicts normal damage on the opponent. If the attacker also has the constriction ability, it inflicts constriction damage in addition to natural weapon damage. "
> -Could it make a second grapple check at +3? For another 1d3 Subdual
> and 1d8 Constrict.
YES, as above.
It can also try to pin his opponent or any other grapple move.
> -Once you pin a target, can you make damage in the same round (after
> the pin) if you can make more than 1 grapple check?
YES, see PH p137 under "Pin".
"If you get multiple attacks, you can use subsequent attacks to damage your opponent".
> SNATCH:
This one is harder. So let's try it one step at a time.
The Dragon does not have the Improved Grab ability, it just initiates a grab like the Improved Grab above.
Also, from MM p.61
"Grappling: Dragons do not favor grapple attacks, though their crush attack and Snatch feat use NORMAL GRAPPLE RULES".
> This is useful for big dragons. If a dragon snatches a creature with its bite, it does
> automatic damage each round, without needing a grapple check.
> -Next round, can the dragon attack with his claws/wings/tail slap AND make the
> automatic bite if it makes a full attack?
Yes it can.
But, as per normal grapple rules, if it does other things than grapple its foe, it suffer a –20 penalty to any grapple checks.
The dragon automatically hits with its bite, so no problew with this. But it suffers the –20 penalty when the victim tries to escape from its clutch. (With all its modifiers, it's almost impossible even with the –20, the Great Wyrm White Dragon has a +61 modifier to its grapple check, -20 it's still +41. Who can escape this?).
> Can it attack the snatched creature with its claws/wings/tail slap AND bite?
> (Kind of tearing it to pieces)
YES, by the rules, a dragon with snatch could do the automatic bite damage AND attack with all its other limbs.
A dragon is a dragon and noone wants to be in the mouth of a dragon. So go ahead, and shread it to pieces.
OPTIONAL: Maybe it could only attack with its 2 claws (4 if hover) and the automatic bite.
> Can it snatch more than one creature at the same time? (1 with bite, 2 with claws and
> still make a tail slap and wing attacks)
YES, but remember the –20 rule for grapple checks only.
The grapple check would still be at +41/+36/+31/+26. Hard to escape!
> If it has hover, can it snatch 5 creatures (1 with the bite, 4 with claws)?
NO.
The dragon is not a monkey and it does not have 4 "hands". So it can only grab 3 creatures at once (1 bite and 2 front "arms").
> Does it receive a -20 penalty to his grapple checks to snatch more than 1 creature?
YES. As per NORMAL GRAPPLE RULE.
A grapple is a grapple. Snatch does not overrides Improved Grab nor normal grapple rules.
> Can the dragon make multiple grapple checks to damage the snatched creature with its
> bite? In snatch it says it's like the dragon had the Improved Grab ability. With a BAB of
> 30 (+30/+25/+20/+15) can the dragon make 4 grapple checks against a snatched
> target (with its bite) and cause 4 bite damage, not using its automatic bite each round?
NO. The Dragon does not have the Improved Grab ability and, as stated under Snatch: "automatically deals bite damage each round", so only once per round.
Snatch also allows (like Improved Grab) the Dragon to deal normal damage in a grapple, but only with a Snatch (instead of subdual damage based on size).
Also, with Snatch, the Dragon can fly away with its prey, and with the Expeditious Retreat spell, it can go really far in one round while doing automatic bite damage each round.
So, this is it.
Let's review this folks.
Val.