Not at all. This is an initial attempt, and might get changed if it doesn't appear to work well in practice. So don't get too attached to your rating.
The rating system is loosely based on the Elo system. After each game the scores are adjusted based on the initial rankings of the players and how well the players did. The adjustment is such that you'll make big gains when winning against opponents with much higher ranking than you and small gains when winning against players with a lower ranking. Losses are handled in a similar fashion.
There are three differences to a basic Elo system. First, the Elo system is for two player games while Terra Mystica is a multiplayer game. This is dealt with by considering each N player match as consisting of (N/2)*(N-1) separate two player matches between each pair of players.
Second, the rating computation is actually done both for players and factions. If you play a "weak" faction and win, you'll get a much bigger ratings boost than if you play a "strong" one and win. Likewise the rating of the faction will be adjusted based on the results.
Third, unlike in basic Elo, the ranking computation is an iterative process. First, all matches are processed in the order in which the games finished. The all matches are processed again, but with a smaller weight. This is done both to calibrate the faction rating information, and to make the order in which games finish matter less. (TM is a much more volatile game than Chess).
That's the idea. But of course that assumes that you care about the ratings, and that you can at least occasionally do well with one of the weaker factions.
The ratings are recomputed completely from scratch every day. Your rating is affected by the rating of every other player and the rating of every faction. If those ratings change, yours might as well.
At the moment all games will count for your rating. But it's possible that at some point older games will start to have a lower weigth. This could cause your rating to decay.
That's a good question. In the original Elo system a 200 point difference in rating between two players should result in the higher rated player winning over the lower rated one 75% of the time. However, it's very likely that the changes done to the system for this site have destroyed that property.
Players with fewer than 5 finished 3-5 player games are completely ignored when ratings are computed. They don't have one, and don't affect the ratings of others.
To some extent. All players will start at a rating of 1000, and there is a limit to how much the rating can change in a single game. So there's a limit to how high your rating can go unless you play a certain number of games. But you should reach an equilibrium eventually.
The stats page has a simple and transparent metric: how often each faction won. The rating system is more complicated, and takes into account more factors. First, it doesn't only look at wins but at all finishing position. Second, it takes into account player strength. And third, it takes into account the strengths of the opposing factions (e.g. the Alchemists never have to play against the Darklings, so the raw win rate of the Alchemists might be too optimistic).