1. Prices vary depending on the game. If I recall, nothing too expensive (and I'm a budget cruiser)
2. As with anything else onboard, sea pass is the currency. If I recall, the sea pass can be loaded with cash in the arcade, but I haven't used the arcade in several years, so this may not still be the case.
3. I never really had an allowance onboard; my parents would allow me free will to decide how much was too much and how little was too little. Usually I stayed within $10 - $15 (per week) at my worst. I eventually moved away from it - I tried to pay for as much of the cruise as I was accountable for and still do. Additionally, since both your teens qualify to use the Teen program onboard, unless they have trouble meeting other teens, the amount of time they choose to spend in the arcade may be limited.
Also consider the fact that RCI offers many other free activities (rock climbing, surfing, swimming, ice skating, etc...) that are all viable alternatives to the arcade and are likely more fun (and not to mention healthier) to do during the day. I know I personally spent more time with those than the arcade.