4.3) Although I had finished a game, my BKR did not change! Is that an error?
No, this is not an error. There are several situations which can be a reason of that:
Both players did not perform at least two moves. It can happen when one player loses the game by a timeout at the very beginning.
You won a game with an opponent whose BKR is significantly smaller than yours. If we would apply the formula exactly, your BKR would have to drop. But BrainKing uses the rule that your BKR cannot drop after you win the game, therefore it remains unchanged. The similar rule applies if you lose a game with an opponent whose BKR is significantly higher than yours.
The game have been defined as "unrated game". Such game is not calculated for BKR.
The game is a part of a match which is not finished yet. The match is treated as a single game which consists of several sub-games. The statistics (number of won, drawn and lost games) and BKR of both players is changed after the whole match is finished and the result is based on the match result itself, not on the results of its sub-games.