Does watching YouTube clips—which may contain music and prohibited advertisements—for the purpose of studying make me an assistant to the one who produced them in sin? And does the ruling differ based on the actual presence of advertisements, or the number of views, or the purpose of watching (necessity or entertainment)?

There is no harm in watching YouTube videos with permissible content, even if they are interspersed with advertisements that contain impermissible elements, provided that one does not listen to or look at the forbidden things in the advertisements and tries to skip them. This is due to the widespread nature of such advertisements and the difficulty of avoiding them. As for the fatwa (definition) mentioned in the question, it pertains to the ruling on subscribing to channels with impermissible content.