In addition, publicly announcing that you have sent a PM is pointless.
Not entirely true. If I request something and I get 10 PMs, I might have only gotten one if the first person publicly announced that they sent a PM to me. With that said, I’m one person who has to deal with those 10 PMs, versus the entire forum reading about the one PM that was sent, so I do understand your point.
You should get an e-mail notification for every user who starts a new private topic with you, not just one, unless you’ve disabled e-mail notifications for PMs.