Does compassion work with Gift of the Life?
Does it work with PK character?
Not sure of the question, however: Gift of life shows the resurrection gump on death, allowing your char to rez themselves but, unlike sacrifice, it freezes your char in place until the gump is either accepted or dismissed. Which means that your ghost can't just run to a safe place to rez as you can with sacrifice.
Compassion gives extra hit points to the resurrected char (other than the char using the skill) depending on level. So, if your mage has compassion at knight level, and rezzes another char, the rezzed char will have (I think) 80% of hits upon being rezzed.
Gift of Life helps your char - Compassion helps others. And Compassion isn't cast, it simply works when you rez someone.
No idea about PK chars.
Apologies for any errors and I hope this helps.