The following represents my reading of the rules. Sometimes I read or remember things incorrectly:
The issue is that kneeling is not a Pathfinder game mechanic, and so is obviously not covered in the underwater combat mechanics. At this point you have two options. You houserule stuff or you find the closest existing mechanics to what your players want to go on. Since you're on the Rules forum, I assume you want the latter.
Attacks from Land: Characters swimming, floating, or treading water on the surface, or wading in water at least chest deep, have improved cover (+8 bonus to AC, +4 bonus on Reflex saves) from opponents on land. Land-bound opponents who have freedom of movement effects ignore this cover when making melee attacks against targets in the water. A completely submerged creature has total cover against opponents on land unless those opponents have freedom of movement effects. Magical effects are unaffected except for those that require attack rolls (which are treated like any other effects) and fire effects.
When touching the bottom, your characters are not swimming. They are not floating. They are not treading water. That leaves "wading in water at least chest deep." The dictionary definition of wade (since it has no game definition) is "To walk in or through water or something else that similarly impedes normal movement" or "To cross or pass through (water, for example) with difficulty: wade a swift creek."
So if you're wading, you can walk. If you can't walk, you're not wading. How do you move if you're too low to the ground to walk? You crawl. If you're crawling, that means you're prone. We have rules for that.
So you could tell them that they can be "kneeling" and still keep their heads above water, but they are treated as if they have the prone condition. +4 AC vs ranged, -4 AC vs melee, -2 to attack rolls, and you can't use bows. Crossbows are fine. Firearms don't really work underwater (see firearm rules).
And yes, they have firm footing.
Situation 2: Again, I'd have to say they're prone. That said, there is nothing stopping them from doing this:
Move action: Stand up
Standard action: Shoot bow
Free action: Drop prone in the water
At this point it becomes a weird game of whack-a-mole with the enemies readying actions to hit the PCs as they stand up. Kinda like how you fight phase spiders.
Hypothetical Situation 3: According to the rules (as I'm reading them), if I find a 5 ft deep hole (assume I'm exactly 5 ft tall), fill it with water, and then start shooting things with a bow, I have total cover from attacks, take no penalties, and can last as long as I can hold my breath.
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If we're talking Fluff/RAI here...
1.) If they're on their knees, to gain that bonus, that seems pretty legit. They would not have firm footing on their knees, as both feet are not on the floor. It seems like they would be dropping themselves to flat-footed and/or prone status to be fair...
2.) If they're that far under, they should be taking penalties to attack for being submerged under water and firing their bow under water. Have you ever tried hitting something on land from underwater? The distortion throws you WAY off(proven on mythbusters!). Assuming whatever device you're using functions that well while submerged to begin with. If the opponents treat them as if they have total cover at that point, then the opponent's should be gaining benefits like +ac vs their essentially blind shooting and attacks being hindered by water. Seems like it would even out for a very lengthy pewpew session.
If we're talking RAW here...
1.) The rules do state the conditions and benefits... therefore they are gained. They are effectively making themselves Prone as there is no Kneeling action. However, since it is 3 feet of water, that's pretty darn close to chest level... so they shouldn't have to kneel.
2.) Essentially they're now considered fighting under water. Go here: http://paizo.com/prd/environment.html and do a ctrl+f and search for Stealth and Detection Underwater. That section, and the Underwater Combat section underneath it will help you a lot.
Actually, kneeling is mentioned in the combat/AC table in the CRB.
It says your AC would be -2 for melee and +2 for ranged, which is half the modifiers for being prone.
Well, I couldn't find it. Disregard my previous post. Looks like your players are fine, although I can't help but feel they shouldn't be able to see things above the water in situation 2.