There are no specific rules for edge cases like this. In Pathfinder the GM is expected to rule in a way that makes sense.
I find in cases like this, combining what's obviously realistic with a check leveraging even tangential RAW that at least nominally makes some of it under the control of the character is good.
The way I'd rule off the cuff if this was presented at a table:
- A six second round combined with falling means no, you don't
automatically get a full attack.
- Pathfinder has a Fly skill.
Most people don't have it, but there is one. Make a Fly skill check -
if you hit 10 you get one attack, and you get an additional attack
for every 5 points over 10.
- This assumes it's a deliberate thing -
like "jumping" instead of "falling" - if a monster did the teleport
as a surprise this check would be 5 points harder.
- You can maybe sub
in Acrobatics, but again at 5 points harder on the check.
Not "no," but not "you can do anything you want just because you asked" either.
A character can damage someone else based on the rules for objects falling on creatures. For most characters, this won’t be much damage and even if you get it to count as a lot of damage, it’s not really an “attack” per se.
Aside from that, the only default rule is the +1 attack bonus you receive for attacking from high ground.
But with the right feats, you can fix that!
Cityscape has a short feat chain in Roofwalker and Roof-jumper, the latter of which gives you extra damage based on how far you have fallen on top of your enemy.
The Urban Class Features web enhancement for Cityscape has a Roof-dweller alternate class feature for the Barbarian, granting these two feats earlier than you usually could get them, instead of Fast Movement.
The Leap Attack feat from Complete Adventurer doubles your bonus damage from Power Attack based on horizontal movement. If you’re jumping from a height, you should be able to cover 10 feet horizontally.
Then Battle Jump from Unapproachable East is the best of them: if you drop from at least 5 feet above your opponent, your attack automatically counts as a Charge and you either deal double damage or count as a size category larger for the purposes of tripping or grappling.
Try to combine these with Pounce or with Tiger Claw maneuvers from Tome of Battle.
For more ways to optimize the art of jumping on your enemies for extra pain, I’ll point you to Little Red Raiding Hood: Guide to the Dragoon.
Best Answer
There are no core rules for falling or diving into water
Right now, this is an area the rules don't touch on at all. It is left completely to the DM.
The only rules listed in any of the rule books for falling in any medium is the basic rule in the PHB and the optional rules for flying creatures and falling from great heights in XGE. Other than that, nothing else is mentioned about water or otherwise.
Jeremy Crawford (prior to the release of Tasha's Cauldron of Everything) confirms this and offers up a personal house rule in this tweet:
As of November 2020, there is now a falling rule in a supplemental book
In Tasha's Cauldron of Everything (p 170) it says:
As with the majority of non-core rules, it is entirely up to the DM if and whether to include it.
Please see this answer for more details.