If an angel or demon has a level 2 Distinction, does he also get level 1? Does the same apply to level 3 for levels 2 and 1?
Yes, but keep in mind that a being has to earn the lower-level Distinctions to get the higher ones, so the point is moot. The only use in not listing the lower-level ones is to save room on the character sheet. A Superior could grant the powers of Distinctions “out of order,” but that would confuse everyone, so they don’t.