Okay, let's talk about those things. Oh, wait, we already have.
Is there "physics" in the game world? Well, there's the physics of the game world, which is to say that there are some aspects that are acknowledged already in the rules.
So if I, as a DM, say, "You fell 30 feet, so you take...", and a players complains, "Wait, you're trying to bring physics into a magic oriented game world", I cast a huge, double-empowered Dispel BS on them before they finish the sentence. Things like falling damage, water pressure, air pressure etc. are already accounted for in the rules. (See Falling Damage, the section of Overland Travel relating to climbing high mountains, and spells like Cloak of the Manta.)
And yet the air pressure does not change the weight of the air in a bag of holding, does it?
So, is there water pressure? Already established. Will water flow into an open and unprotected container if you immerse it?
Sorry, but that last question was so stupid that I threw up in my mouth a little while typing it. We shouldn't have to even ask it, but some people don't like the answer and try to invent excuses to question the obvious. (In fact, I have a bet with myself that someone will try to argue it, even now. "What if it's upside down? Why would it work across dimensional boundaries. Are you sure there's air in the game world? What if it's a Tuesday and I have a Royal Fizbin?"", etc. )
"Is a Bag of Holding the same as a mundane container in this regard" is the real question, though. How permeable is the aperture between our dimension and the non-dimensional space within the bag?
Now, to more serious questions: Can you use the bag as an air supply? Yes. the rules say so.
Actually, the rules say a closed bag with a person in it can support that person for 10 minutes, regardless of the capacity, used or unused, regardless of the size of the creature/person, always 10 minutes of air. That seems inconsistent with physics. It's a close enough compromise for gameplay, but then again so is "something must either pass through the aperture or remain on one side so you can't stick your head in there indefinitely but liquids don't flow in".
Why do all bags have the same amount of air? I rationalized an explanation, but the real, according to RAW, unarguable reason is because the rules say so. Come up with the in-game explanation of your choice.
OK. How about "because all bags of holding hold air sufficient to sustain a creature for 10 minutes, replenishing same whenever the bag is opened". Now, that seems to fly in the face of "oh, it's all full of water now", doesn't it?
Will air pressure change the amount of air in the bag, and thus change the weight of the bag? Since the rules say that the bag doesn't change weight when you add things, I'd say it doesn't change weight when you add things. Even something as dense and massive as air. Of course, the air in your game world may be more massive than the air in my game world, so you'd better check with your DM.
I'm not discussing the weight of the bag with air in it, but the weight of the air in the bag. You're weighing it down with water, but air is not weightless, nor is its weight a constant. So why does the weight of the air not change, thereby altering the remaining weight the bag can hold? Perhaps because the air in the bag is a constant and it doesn't allow other media to flow in automatically. "The only answer?" No. But not an answer with no merit either. The fact is, we are dealing with magic, and magic by definition defies the laws of physics. It's bigger on the inside than it is on the outside. Its weight is a constant regardless of what is placed within it. A scruple over the limit and it is destroyed. None of that is consistent with real world physics, so real world physics is not the only reasonable basis for a ruling.
Will a bag sink? By the rules, a person with 15 pounds of gear will sink if they fail a swim check. The lightest/smallest bag weighs 15 pounds all the time, and can't make a swim check.
I submit that a person carrying 30 pounds of cordwood strapped to him will not sink based on the laws of physics. Does that mean, in your game, they will? What about 15 pounds of stout leather, sufficient to make a huge inflatable bladder, full of air? Does it sink or float? If I dive under a ship, then grab it, and next fail a swim check, does it sink because I am carrying far more than 15 pounds of gear and I failed my swim check? That sounds pretty stupid as well, but, as you said, "By the rules, a person with 15 pounds of gear will sink if they fail a swim check."
Will the amount of air inside make a difference? No more than the amount of gold or anything else. We could get into air displacement v fresh water v salt water, but since the bag changes neither size nor weight whether full or empty, it doesn't matter. The inside is a non-dimensional space (not actually a separate dimension, just a space that takes no space), so whether it's air or lead, it doesn't displace any water on the outside.
As I said, it's the weight inside that matters. But let's look to your SpandexBag again - why could that magical spandex not expand just enough to hold the weight the bag is capable of holding, requiring someone exert pressure to push it over the limit? Is that somehow illogical magic? More illogical than a bag that is bigger on the inside than the outside and whose weight outside never varies?
If we make the bag invisible, can you see out of it? That's actually a really good question. Since your head is still ijn the same dimension (bags are non-dimensional, not extra-dimensional), the answer should be yes. But because of the spacial distortion that comes from having your head take up no space, the answer is really anybody's guess. And by that I mean, it's the DM's call.
According to
http://www.wizards.com/default.asp?x=dnd/rg/20051101a, those nondimensional spaces are also extradimensional.
Now, what happens if the portal to the non-dimemsional space closes while something is part way through. I'd say, see
Gate. Whatever the rules say there is what I'd apply.
I don't believe there is any indication of what happens if a gate is closed when something is part way through. It says "anyone who chooses to step through the portal is transported" and that "You may hold the gate open only for a brief time (no more than 1 round per caster level), and you must concentrate on doing so, or else the interplanar connection is severed.", but doesn't speak to anything being part way through.
Now, one other interpretation would be that, just as we don't count your hands as you place things in, and remove things from, the bag, and we don't count the air within the bag, we do not count any medium which fills the bag, only things placed in the bag within that medium - so you can fill it with water without contributing to its capacity. Not my preferred ruling, but a potentially viable one - especially if we are playing an underwater campaign and decide to assume water, not air, is the default medium.