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1.The rule does not say that the rider falls down. He is still on the horse, the rule is clear on that point. He 'counts as fallen down' (aargh!) Since this is the Knocked Down equivalent on the injury chart, we have always treated it as such. Thus any subsequent attacks do not need to hit only wound, etc.
We allow Step Aside and Dodge as the rider can do those things while mounted and they are a hallowed element of equestrian fiction. A similar case can be made for including Jump Up although given the respective wording of the Whoa Boy Table and the skill its a bit more of a stretch.
We encourage mounted models (unlike the rules) so we would allow Jump Up to be used. If your group doesn't encourage 'un-Mordheim' behavior you might not...
2. Your question makes it sound as though #2 follows #1 as the same circumstance. In that circumstance, the player rolls a 1 or 2 on the Whoa Boy Table, no, the enemy warrior must roll to wound the rider. If the rider is Stunned AND the horse doesn't bolt, then the enemy warrior MUST attack the horse. (My kingdom for a horse that doesn't bolt!)