3.3.1) When I click a piece to move, it automatically performs a sequence of jumps, although it seems that I can choose from several different jumping paths to do. Why wasn't I given a choice?

It means that the automatic jump was the only possible move in the situation, regarding special rules of the particular checkers version you are playing. For example, you are obliged to make the longest possible jump (i.e. capture the maximum number of opponent's pieces) in International Checkers and since BrainKing can detect such a situation, it would not allow you to make any other move.