I agree that greater clarification is required in the area of evasion, fleeing and pursuit. The same situation and resulting debate has arisen during games at my local club. We decided that cavalry choosing to flee as a response to being contacted cannot turn and shoot in the following shooting phase, but their pursuers can if they are within range. This seems to work well. We've always allowed Mongols to shoot backwards with 2 out of 4 stands after a flee response move.
Evading cavalry still face their attackers and can therefore still shoot. In the updated H&H version we have made all evade moves 2 hexes instead of 1 (E1) or (E2). A number of players felt that it was unfair to give some cavalry a greater evade distance than others - and unnecessary differentiation perhaps!
We will release the H&H update as soon as we can - the forthcoming release of the WW1 Raging Empires draft version has been a bit of a distraction and caused a few delays - sorry about this but we are getting there!