1. No, Qi alone does not indicate skill, but neither does win-ratio when you're a new/semi-new player and might win some matches by pure luck. So to get a more accurate ranking you need to take both how long you've been playing, which can be measured by your Qi and what your win-ratio is, into account. A ranking system purely based on win-ratio would be just as fail as the old one.
So while it does not necessarily indicate skill you still have to incorporate it into the calculation to give you a more accurate result.

2. How exactly would the fact that Qi determine your belt have any effect whatsoever in this matter? I honestly can't see what the problem is there.

3. The only thing problematic I see here is that it can be bought. Maybe there is a way for the program/whatever handling the ranking to differentiate between bought Qi or earned Qi? If not it wouldn't really matter, as long as all the qi you buy is handled as losses, which would suck for the ones buying it, but wouldn't really affect the ranking unless a large amount of players would buy qi.