The ring falling off was actually a nod to the regeneration from first to second Doctor. Troughton's Doctor notes that his ring does not fit anymore. The first Doctor used the ring on occasion to hypnotize people.

Capaldi's Doctor wore a ring to hide his wedding ring, which he apparently can't get off anymore and wasn't about to destroy.

Really, I'm going to guess Testimony nabbed a copy of Bill after she had a hole shot through her chest. The Pilot never would have seen any of it, or just may have allowed it.

Honestly, I was more disappointed it was Bill and not Susan they brought back. Susan would have been a better call-back. I've always wondered what happened to her (and maybe her descendants?) after she was left behind on Earth.