To be clear, there are lots of different ways the Paladin can gain Valor. It seems like you are only interested in the Valor gained from the Paladin's
Chivalrous Challenge ability. In which case, this is the relevant text: "If the Challenged enemy attacks any other object, gain 1 Valor." Any other object refers to any object besides the Paladin. So now lets look at your questions.
1. If the adversary mage casts an attack spell targeting a creature other than the Paladin, does the Paladin gain valor?
Yes. Attack spells count as an attack. Thus the enemy has attacked another object, be it a creature or a conjuration, other than the Paladin fulfilling the requirements of the Paladin's ability.
2. If the adversary mage casts a zone attack spell, does the Paladin gain valor?
I can see why you may think the answer to this is no, since the Zone Attack targets the zone which is not an object. However, the Zone Attack is comprised of multiple attacks which are hitting the various creatures and conjurations within the Zone, and these attacks still count as originating from the caster. Thus, each of these attacks is fulfilling the requirements of the Paladin's ability and will generate Valor.
3. If the answer to the second question is yes, how much valor does the Paladin gain? Just one or one for each attacked creature different from the Paladin?
Kind of already answered this, but just to be clear, each and every creature and conjuration attacked by the Zone Attack will generate a Valor for the Paladin. Every single object that your Challenged enemy attacks generates a Valor for your Paladin, other than the Paladin himself.
