Esther actually does marry Mr. Jarndyce.The way she writes about Allan Woodcourt does not sound like his happy wife; it sounds like a lonely, painfully repressed woman longing for something she never had. What if Mr. Jarndyce didn't really let her go? What if he married her, treated her as kindly and lovingly as possible, and still couldn't make her happy? Esther, being Esther, would hate herself for being (from her own warped perspective) "ungrateful" and "failing in her duty" and find it impossible to tell the truth even in her secret memoirs. In this case, the cut-off sentence at the end ("They can very well do without much beauty in me, even supposing - ") would be due to Mr. Jarndyce, Ada, Charley or one of the children catching her, and hopefully confronting her until she finally lets her suppressed emotions out.
Inspector Bucket is a Changeling a la Star Trek: Deep Space Nine.He's devoted to the law even at the expense of compassion (taking Jo away from Bleak House, pursuing Gridley) because of his inborn Changeling drive to keep order. He appears out of nowhere because he can shapeshift into shadows and furniture. And the reason he calls himself "Bucket" is because, like Odo, he uses one to regenerate.