Good for you, welcome to the club!
Hmm, so I guess not
full keg then, eh?
I'm a little confused about this. Is the plan to store the kegs of beer at room temperature, and then on nights when you plan to drink some, you'll move them into some sort of cooler, dump in a bunch of ice, and try to chill the whole thing down? Then what, let it warm back up again the next day? Can you clarify this part of the plan?
Do you have a refrigerator in which you can keep the kegs cold, even if it's not outfitted with taps?
There's no benefit to carbing extra-slowly. Just set them to the proper pressure right off the bat, then wait a week or two and they'll be fully carbed. Note that the "proper pressure" depends heavily on the temperature of the beer. I keep my kegs in the fridge at around 34 F and just leave them on 12-15 psi of CO2 at all times.
That sucks, but if it makes you feel better, every kegger's been there. It's almost a rite of passage.
LOL, why, what are you worried about? CO2 isn't poisonous, you're exhaling it right now. You're dissolving it into your beer, but you're worried about inhaling it? Granted, if you inhale an atmosphere of nothing but CO2, you'll pass out, but at the rate of a slow, week and a half leak from a 5 lb tank, the amount would be totally negligible compared to the amount just floating around the atmosphere anyway.
As another poster noted, there should be some sort of nylon washer that sits at the connection between your tank and the regulator (unless your regulator has an integrated O-ring, as is the case with my Taprite regulators). After that, make sure all your hose/fitting connections are as tight as possible. Make sure the posts on your keg are snugged up nice and tight. Finally, make sure the pressure relief valve on your keg lid is screwed on tight.
After checking all of that, get yourself some keg lube, and use it on all rubber O-rings in your keg, especially the big one around the lid. That stuff is magic. Finally, once you've tighted every connection, snugged down every post, and lubed up all your O-rings, put the whole thing under pressure and get yourself a spray bottle full of Starsan and spray everywhere you could potentially have a leak. Look for bubbles. That's where your leak(s) is(are).
I'll defer to the expertise of others on this one, but count me as one who was unaware that there could be two grades of CO2. CO2 is just what it is - CO2. It's a gas, a molecule. You can't make different CO2 depending on the use any more than you can make different oxygen (one for welding, one for scuba diving). It is what it is. I get my tank refilled at a place in town that fills fire extinguishers, and they've never asked me whether I wanted "beverage grade or industrial grade." They just give me CO2.
It oxidizes the beer, giving it that "wet cardboard" taste. If your tank hit 0 while it was connected and open, then you have no pressure in your kegs. However, assuming you properly purged the kegs when you first hooked them up, then there should be very little oxygen in the kegs, and they would instead simply have CO2 in their headspace. No pressure, but still just CO2. If your leak was on the tank/regulator end of things (i.e., at the tank/regulator connection, or the hoses), then the kegs should be fine, and that CO2 will sit in there indefinitely. If, however, your leak was at the keg itself (i.e., post not tightened down, leak at the lid O-ring, etc.), then there will be a tiny amount of gas exchange occurring, slowly replacing that CO2 with regular air (i.e., oxygen). But the amount/rate will be so low as to be negligible. I wouldn't worry about it, just DON'T OPEN THE KEGS until you get that tank refilled and identify and fix the leak.