Drilling tanks are sooooo easy. I have never heard anyone actually complain before in how hard it is. I have drilled literally hundreds of holes. Tooo easy. and no you do not need a drill press. And yes you can drill a tank that is up and running. All you have to do is drop the level of the water and then drill. I have done it before, too easy.
You do NOT want to use a dremmel. That is way to slow and just a serious PITA.
Use a diamond bit and use a drill guide. Use a spray bottle to keep the bit wet and if you are drilling from the inside out, clamp a piece of wood on the out side and use a small powerhead or a spray bottle top to suck out the tank water and spray the bit for lubrication and moisture. The glass pieces is nothing more then silica sand that causes no problems for the tank.
Drilling does void the warrenty, but if you don't approach it with seldgehammer mentality, then it will work out just fine.
Final note, do not drill glass tank bottoms, they are tempered.
P.S. If I lived in your area, I'd charge you $15 a hole and have it done in less then 5 minutes. And you wouldn't have to drain it, as long as it wasn't up against the wall like Ed Hahn's tank is.