This is a measure of your performance in all your Madness matches, whether you play them in the Madness Cup, or a one-on-one match against a friend (Madness Duel).
Your rating starts at 1200 and goes up when you win a match, and down when you lose. If you've ever played online chess, it's the same concept.
That depends on your rating and the rating of your opponent. If you beat a highly rated opponent, you rating goes up significantly. If you beat a lower rated opponent, your rating goes up, but not by quite as much.
We used a simplified version of the Glicko-2 rating system, which is also used by major chess and other gaming sites.
You can win these in the Madness Cup or Madness Duel matches. They count towards "Levelling Up" and your overall site rank.
No, you can only gain Madness Points, they never go down.
The Madness Cup prize pool is seeded with 1000 Madness Points for each participant. Thus if 450 players are in the Madness Cup, there will be 450,000 points in the prize pool. All players who make the bracket section of the tournament are "in the money". The points are given out in a percentage-payoff format, just like a Multi-Table Tournament.
You get 100 Madness Points for winning the match. You can also get up to 100 more bonus points for your margin of victory in big blinds. For example, if you win 43 more big blinds than your opponent during the match, you will get a total of 143 Madness Points for the win.