She specifically said that her parents willingly gave her to her Watcher to be raised.  They were alive, but had no more contact with her after that, as far as we know.

Kendra's parents turned her over to her Watcher as a child.  She said that her culture had more respect for the traditions.

It's a great episode.  I'm one of the few who found Angel to be a much better show than Buffy, and this was one of my favorite episodes of the series.

Why would they?  Who says either one gives a shit about the other?  Jasmine is much more about uniting people than she is about doing away with evil. She never mentions being anti-evil.  She's not running around randomly killing "evil" things.  She's amassing her minions.

Willow helped with a spell to try to get the amulet back, but I don't remember Anya explaining what the amulet did.  The spell was unsuccessful, anyway.  Anya was recreated as a vengeance demon by T'Hoffryn after Xander left her at the alter.  There was never any mention of a new amulet, as far as I remember.