Just like using a wall adapter, but you don't have to plug it in to the wall. I don't own one so I can't say on the recharge time, but I can comment on the capacity. It's a lot. Most people use less than 1000mAh per day so it would run over 8 days on a charge. That's a lot of juice (as in electrcity). As a sparky myself, I've always refered to electricity as juice so it's weird for me when people say juice in reference to e-liquid. There's actually a reason people refer to electricity as juice. In the old days before quantum mechanics (discovery of the atom), they thought electricity resulted from fluid movement through a wire and referred to the fluid as "juice". The bigger the battery, the more juice it could hold. They were sort of right, just electrons instead of fluid, but the nomenclature stuck.
I didn't see any specs on the max current output for that power pack. For a 3Ω at atomizer at 5V, it needs to be able to put out at least 5V/3Ω or 1.7A.