This page contains detailed information about Jayne as obtained and inferred through quests. It is organized by volume, and the quest(s) where the information was obtained is linked. If the quest was fealty-specific, that is noted as well.
Feel free to add new information as you find it!
If you have not played through all of the volumes, this post will contain spoilers.
Jayne and her parent (your late spouse) used to take country rides together. A Time to Mourn
Jayne apparently attempts suicide early on, an act of defiance against her new position and the requirements of it. A Time to Speak
After you reveal the truth about your background to Jayne, she becomes more complicit as your heir, finally beginning to understand what needs to be done as head of a household. The Heart of the Matter
She is happy that you looked after Gammer and hopes to do the same with her own advisors. Queen of her People