Question: Why were there no rings exchanged during Bernard and Lydia's wedding ceremony?
Question: Who is Scarlett? She appears to live with Charles, but not share a bed with him; IMDb refers to her as Charles' sister, but her, er, style of talking is so out of kilter with Charles and indeed all the others that it seems unlikely that she's related.
Answer: According to a deleted scene, she was found passed out drunk under the kitchen table after a party that Charles hosted and never got around to leaving. She's now his lodger, presumably paying rent and a share of the bills.
Question: Why wouldn't Charles' brother be his best man? Or is that not traditional in England the way it is in America? It's not mandatory but is certainly expected, unless the brothers are not close (which Charles and his brother are) or the groom's father serves as best man.
Answer: A groom can choose whoever he wants as best man. As you say yourself, it's by no means mandatory for it to be the groom's brother, even if they are close. In this particular case, it's possible that David felt that he ought not to be the best man, due to the difficulty that he'd have in making a speech, but, really, Charles was under no obligation to choose him.
Answer: The priest had so mangled the entire ceremony that this was just one more blunder.