1. Vampires may skip a scene for each point of stress, successfully make a Discipline check at the end of a scene in which they use their powers to clear it (which seems odd to me, but w/e), or kill someone by feeding on them to clear the track in one scene.
2. Yes, you have to use an ability to make a check.
3. The book is saying that your vampirism powers do not depend on feeding, as most of them are related to feeding--it would be kind of silly to have to feed in order to be able to feed...endless cycle of destruction, there. However, at least 2 refresh points' worth of powers must be taken in other, non-Vampiric categories, and at least 2 refresh points' worth of these powers must depend on feeding. For example, you could not take only Emotional Vampire and Shadow Cloak, because Shadow Cloak only costs one refresh point. However, you could take Emotional Vampire and Supernatural Toughness.
4. This one might be up to GM interpretation, but as I understand it, a sufficiently stressful or emotional situation can call for a Hunger roll. The difficulty value, I think, is half of all your powers that depend on your Feeding Dependency. That is how I interpret "the affected powers." However, it might also refer to only the powers that have been 'lost.' If the second interpretation is correct, then so is your example. If the first is correct, then you would have to check for feeding failure against half the value of all your abilities that depend on your Vampirism.
Hope this helps!