1. Yes, that is most likely the reason. I'm not an expert with familiars as I didn't really use them when I had them. But yes, try killing the badgers with your wolves and not familiars.
2. Last I checked there really isn't anything determining how many predators are on a level. They are usually random and prey depend on the season. Obviously they are harder to find in winter and fall but easier to find in summer and spring.
3. Yes, to earn BE(Battle Experience) the wolf has to kill something. If you have four wolves, only the wolf who kills the prey/predator gets the BE