Just focusing on the technical parts of it, as far as I'm qualified to say anything:

a)
With satellite connections the lag for the Ochotnik operators would be closer to .4 and up to .6 seconds (which, technically, could still be counted as "500 milliseconds" but it would still be misleading by two orders of magnitude). That is, assuming that they are using geostationary comm sats (and possibly one for relay); GEO is .13 light seconds away, so merely going up and down is .26 seconds already. Add a relay, that's another .14 light seconds (assuming that you have six and not just three in orbit). Of course you could also have comm sats in low orbit but then you'll have service interruptions as you need to hand over from one to another. Solvable, sure.
Add to that the lag for digital video compression. The better the compression, the more lag it causes (but you save on precious bandwidth). A good compression may require the analysis of five consecutive frames; even at 60 fps that's another .083 seconds of lag. And that's really a best case assumption. My cable TV is lagging about 15 seconds behind, and IP TV's "live" coverage of sports events can be more than a minute behind.

b)
With 3 x 90kg RDX detonating in semi-enclosed space plus demolition charges and a partial collapse of the cave, it's going to stay pitch black for the two girls for quite a while. In fact, I think they're lucky to be able to open the blast door. If it's heavy enough to withstand the direct impact, it must be machine operated. If it can be opened by muscle power, no way they're going to survive it. The problem here is that you're not dealing with a pressure wave in the open which quickly dissipates, but one that is confined in all directions but the cave entrance, with plenty of shockwave reflections.
Even a single hand grenade (80g RDX) will create so much dust, you can't see anything in a room for a minute or so after it went off. Granted, the cave is bigger - but the missile warheads contained more than three thousand times as much HE filler.