A creature's movement provokes attacks of opportunity normally during mountain avalanche

To this reader it seems that a martial adept that initiates the 5th-level Stone Dragon maneuver mountain avalanche [greve] (Tomo da Batalha 84) provokes attacks of opportunity normally due to her movement.

However, keep in mind that a typical creature's movement—no matter where to, what kind, or how much—only provokes an attack of opportunity from each typical foe once per round. So, for example, while the martial adept may provoke from enemies for leaving a square those enemies threaten to entrar an enemy's square, the martial adept won't typically provoke a segundo attack of opportunity for her movement from those same enemies for saindo that enemy's square.

O Manual do Jogador on Attacks of Opportunity, in part, says

This feat [i.e. Combat Reflexes] does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you—such as by moving out of a threatened square and then casting a spell in a threatened square—you could make two separate attacks of opportunity (since each one represents a different opportunity). Moving out of more than one square threatened by the same opponent in the same round doesn’t count as more than one opportunity for that opponent. (137–8)

For example, a human martial adept faces off against a kobold that possesses the feat Reflexos de combate and that's armed with a longspear and wearing spiked armor. She takes a full-round action to initiate the mountain avalanche maneuver, and, as part of that maneuver, begins moving. She enters the kobold's threatened area, not provoking an attack of opportunity.

Then the martial adept continues her movement but dentro the kobold's threatened area so that she's adjacent to the kobold, provoking an attack of opportunity from the space she left due to the kobold's longspear's reach. The kobold makes that attack of opportunity and misses.

The martial adept's movement thus far resolved, she continues moving, traveling into the kobold's square. (This is not normally allowed, but the maneuver creates an exception.) Were it not for the Manual do Jogador clarification, this, too, would parecem to provoke an attack of opportunity due to the kobold's armor spikes, but the martial adept's movement is here merely providing the kobold mesmo opportunity it already had—an attack of opportunity due to the adept leaving a threatened square. The kobold can't make a segundo attack of opportunity against the adept. The martial adept stomps on the kobold with impunity, dealing it the mountain avalanche maneuver's damage.

Then the martial adept continues her movement, exiting the kobold's square Além the kobold. Since creatures that wield nonreach weapons—like armor spikes—threaten their own spaces, the martial adept would seem to provoke from the kobold a terceiro attack of opportunity, but this is still just movement on the martial adept's part, so the kobold doesn't get another attack of opportunity against her.

To be clear, a creature can't normally percorrer a foe's square, but doing so is specifically allowed by the maneuver mountain avalanche, and its specific rules cover what happens when the adept does. Unless the martial adept only occupies a some of a big creature's space as the maneuver describes, entering the creature's space due to the maneuver doesn't itself offer the foe a novo e único attack of opportunity—only the movimento provokes, and, as described above, it provokes normally, typically only once per foe per round.

"Okay, but this still sounds like a pretty terrible maneuver. When would it be useful?"

In a campaign I'm running right now, Shady Stu is a level 14 mishmash of pugilist, scout, swordsage, warblade, blade dancer, shadowdancer, and totemic demon slayer with a speed of about 150 ft. and a Tumble skill modifier in the +40s. Stu could use this maneuver to murder whole villages. (He wouldn't, though, unless they were mal villages; he's a good guy.) For some players, I imagine that alone makes the maneuver appealing.

However, I'm guessing there's no Stu (or a character like him) in your campaign, and if there's not, generally, you're right: this maneuver isn't very useful. Its damage is, at the level it comes online, very nearly insignificant (even if it is almost guaranteed), and the risks that come with it can be… excessive.

Nonetheless, many martial characters that specialize in melee combat lack completely any way of affecting multiple creatures with their attacks. They've to hope to be surrounded by a horde of enemies if they're to take out more than one per turn. Further, there are DMs who throw hordes of weak creatures at their PCs, maybe hoping those weak creatures will soften up the PCs with the occasional natural 20. Those weak hordes still need to be dispatched, and the wizard can only cast each day so many bolas de fogo. In such campaigns—likely the same campaigns wherein PCs consider the feat Great Cleave a valid lifestyle choice—, the mountain avalanche maneuver may be an attractive, if overpriced, choice.

There's nothing in the Mountain Avalanche maneuver that overrides AoO.

So the text reads:

If you move over only part of the space a creature occupies (for example, you are a Large creature moving over half the space of a Large opponent), it can either attempt an attack of opportunity against you or it can attempt a Reflex save (DC 15 + your Str modifier) to avoid half of your trampling damage.

The format is strange, but if you remove the content within the parenthesis, then it reads pretty standard. If you enter into their space, they can choose to save or hit. However, you'll still trigger the AoO when you exit the initial space. Its essentially an improved Bull Rush. Unlike the Bull Rush action, looks like they can't attempt to stop you. Like the bull rush mechanic, if they have allies near them, they get AoO too.

Its a good maneuver, but its used in very specific situations. It has the potential to let you attack 12 times in a single round, and the fact that the enemies cant physically stop you means that you can get past the grunts and right beside the big bad. Its probably best used with a lot of armor and a shield. If you have a Magic User ally, ask them to cast blindness on your enemies, which will allow you to attack all the blind enemies with no AoO.

Não.

I don't own this book (disclaimer) but per este link:

Casting Time: 1 full-round action

...

"You must move into every square a creature occupies to trample it."

The rest of the rules are similar to trample (which is in the SRD and I prefer to cite; see the first link or other answer for an exact quote on the maneuver):

If a target’s space is larger than 5 feet, it is only considered trampled if the trampling creature moves over all the squares it occupies. If the trampling creature moves over only some of a target’s space, the target can make an attack of opportunity against the trampling creature at a -4 penalty.

My read of this is if you trample (avalanche) the creature in its entirity it does not even get a first an AOO for trampling (avalanching). And since the only action is trampling (avalanching), there's not even a second action to provoke an AOO.

Similarly if folks had weapons and you trampled (avalanched) by them (as opposed to on them) you'd just get a single AOO (not one for trampling (avalancing) and one for moving).

But for thoroughness on second AOO, from Attack of Opportunity (SRD):

(Combat reflexes) does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you, you could make two separate attacks of opportunity (since each one represents a different opportunity). Moving out of more than one square threatened by the same opponent in the same round doesn’t count as more than one opportunity for that opponent.

But again this is not applicable because both trample and avalanche maneuver take movement into them making them a single item; it's not move then trample/maneuver.

Nothing about combat reflexes grants you the ability to AOO when one is not normally presented.