A: I wouldn't advise it. I've seen some nasty mold breakouts from tap water. Only use distilled water. It's about $1 a gallon at your local store. That should last you quite a long time. In my experience, a gallon goes a long way.
A: You certainly could do that if you wanted to. The Power Stick has a screen over the holes to prevent the crystals from escaping or directly touching your cigars. However, a product that is slightly better suited for a jar would be the CI Smiley Crystal Gel Humidification (round). This unit is easier to mount to the lid of a jar, which also allows the humidity to fall downward.
A: 65% is a pretty good spot to be at. I prefer a lot of my cigars within the 65% to 67% range. If you think it's off, it wouldn't hurt to check it. And yes the air where you live can have an impact. Just be sure to not allow your crystals to shrink too much. You should check them regularly, every couple weeks. If you see things start to fall off consistently, then I would consider buying another stick to compensate. As a side note, the less cigars in your humidor, the harder it is to keep your humidity levels higher (more air to humidify).
A: We're pretty awesome, glad you agree! I kid. But seriously I wouldn't use bottled water. I've talked to some people that do, but for me it isn't worth the risk. Especially since distilled water is so cheap to pick up at a local store, and tends to hold you over for a long time.
A: Power Sticks are basically crystal gel jars in the shape of a cigar. They last about 1 year. No water should leak out as the crystals will expand and absorb it. The only trouble I've seen people have is when they soak the piece in distilled water to the point where the crystals explode out because they don't have any more room to expand. If you follow the instruction you won't have an issue like that. Power Sticks are great for 50ct and below humidors where you want to save space and don't have room for a jar.