Well, it does add to the ambiguity of Dooku's position, given that the movie has been teetering over whether Dooku is a villain or not (Padme thinks he is, but the Jedi disagree, but we then just saw him plotting with known villains). The scene also works given that it does a good job of establishing Dooku's character (he masks his manipulations and ruthlessness with politeness). Whether connecting Dooku to two previously established characters paid off in the end or not, it was a backstory and it didn't harm anything either. Also, it contextualizes the duel with Yoda, making it more then just two people with no ties fighting each other.
Debatable; we only saw a fraction of their interactions (and patience didn't seem to be Kenobi's strongest suite with Anakin's outbursts). On the other hand, even if we did want to assume that at least some of Kenobi's taking the blame for Anakin's downfall was him being too hard on himself, his attitude with Yoda when stating his intent to train Anakin in TPM does fit pretty well with his reflections in the originals.