So, I'm going to give you slightly different advice from William -- you can choose to be confused by this, or you can just decide what you wanted to do in the first place and then point to whichever one of us happens to tell you to do that and say "I'm following expert advice!"
If you have money to burn, go ahead and buy a new, fancy charger. If you've got a local hobby shop that caters to electric RC pilots and has a good reputation with them, just walk in, put your battery on the counter, and say "I want to charge this, what should I buy?" If they're confused by the fact that you fly on strings just tell them that your system has about the same power demands as a 3D RC plane of the same weight. If you have any RC friends who fly electric start buying them beers now so you can lean on them for help later.
If you're on a budget, just use what you have until you're sure you like this control line stuff. Then you can worry about upgrading.
Unless the charger you have is appallingly inefficient then it should not be taking 3A in to put out 2A at 12V -- so your 3000mA adapter box will probably do. If it doesn't, turn the charger down to 1.5A or 1A and be patient.
If you charge the batteries fully and leave them lying around for months then they will lose capacity. I don't think that you'll harm them much by leaving them fully charged overnight, or even for a few days. This gets down to how finicky you are -- for now I think your biggest worry should be smacking dirt, not puffing batteries. If I'm wrong then send some curses my way and buy some new batteries at Hobby King.
Once you get the plane done you'll have a poor-man's discharger. Just run the thing for about half a flight's worth of time while hanging on to it. If you want to be finicky, do so at reduced throttle setting, or with a one-inch smaller prop on the thing. Don't cut your fingers off.
As far as potential danger, you should always store your batteries as if they'll burst into flame at any moment. This isn't because they do so very often (they don't), but because you don't want your house to burn down with your loved ones in it, or worse, your shop to burn down with your planes in it. Once a LiPo catches on fire it burns very intensely -- it carries its own fuel and oxidant and it's in a thermally insulating package, so there's no way to take away any of the three things that fire needs to keep going. So, store the batteries in a container that'll let them burn without taking the building it's in with it, or store them outside. (I violate this rule -- I need to get me a fire proof bucket or something, or one day you'll be reading one hell of a sob story here, starting with "I was stupid").