Nice score. That's one of the expensive bits.
1) Yes. You need a carbonator cap. It's also possible to build one yourself using tire valves and such. It's more difficult with the less liquid you have. Sometimes it's easier to have a 16 oz bottle to recarbonate soda in from a flat 2 liter, if you drink that slowly like I do.
2) Yes, its possible. It's sort of tough though. You want to see about finding the various salt and mineral contents of those waters and try to replicate them. There are a few books about this subject, but few websites. It's also how carbonated mineral water was originally delivered to people (other than consuming it at the source). I don't know the carbonation content of those, but you can certainly vary your carbonation to achieve it.
3) What do you mean by gas bottle? And when it's said to remove the air, what you really want to do is fill the plastic bottle by using the carbonator cap, pressing the valve and squeezing the bottle, then pressurizing the liquid. This way, only carbon dioxide is in the liquid and will mix into the liquid. If you mean glass, then no, it's not recommended. If you want to use glass, you essentially need to carbonate the liquid, then cold fill the bottles. I haven't seen burst test results on glass, and theres varying opinion on certain non-soda bottles.
Secondary: GF Czech Lager
Waiting to be kegged, Italian Primitivo
Kegged&Ready: GF Orange&Coriander, GF Honey Lager, GF chocolate ale, GF English ale, Island mist (zinfandel), Island mist (cbry malbec).
Bottled: Infected Mead, Dry Hard ciders, Accidental Sorghumwine, various unnamed.