There's usually plenty of air underground in a cave. They are actively being weathered / formed by little streams, which drag down air with them, forming a natural circulating draft. So even though the human-sized exit is flooded, there are likely to be multiple small inlets + cracks in the rock. The situation is very different in an (artificial) mine, which often have a single entrance/exit and no flowing water, so the air is totally stationary and quickly becomes stale.
Airbells, which are small air pockets in an otherwise flooded section are relatively unusual, and from the video footage it looked like the football team had climbed up into a larger Fossil gallery overlying the current (active) flooded section. Hopefully this means they will also be well protected from any future more extreme flooding.
These little stream inlets form a source of drinking water. Even when the main cave river is a turbid mess, there's normally plenty of clean little streams coming in - some of which will be fed by percolation water (seeping through rock) and therefore effectively 'mineral' water.
Often when journalists describe caves in the press, 'one kilometer underground' would be better described as 'one kilometer into' the cave. Certainly the cave doesn't look very deep, most river caves form fairly horizontally.
For digging into or exploring from above, what matters much more is how thick the rock is above them (or above a chamber that they can reach), and what it's made out of.
Locating them on the surface (i.e. figuring out where to start digging) will also be a challenge - most caves are not surveyed with a high degree of accuracy, and doing so through a flooded, flowing, low-visibility section is extremely difficult. (One of the rescue divers, John Volanthen, has done some pretty amazing stuff with a water-proof data-logging accelerometer + flux compass in this area - the "Lazy Boy Sump Mapper".) They will probably dive a radio beacon into the cave + then use that to locate the party, combined with a (dry) survey within the cave to figure out the extent of the available space to the survivors.
Radio comms should be setup quite soon - one system which may be of general interest to the Hackernews community is the cave-link:http://www.cavelink.com/cl3x_neu/index.php/en/It has a lot of automation + resending / checksumming of messages to enable transmission over the very low bandwidth and noisy VLF channel through hundreds of metres of rock.
