Because of the direction. I read that current flows only from anode to kathode of a diode and cant flow from kathode to anode. If thats not the case maybe nothing would change if i reverse them.
The transformer outputs AC.
In the original schematic, assuming node B is 0V, D1 conducts when the AC cycle is positive and D2 conducts when it's negative. If their polarities were reversed, then this would be the opposite.