A good way to start is to look at Frogbeastegg's guide:
https://forums.totalwar.org/vb/showthread.php?t=38382
It has a lot of good info, and near the bottom are the temple characteristics.

Concerning new family members, I think there is still some debate about family growth. A lot of people think the family grows as necessary (if you lose a lot of members, they get replaced pretty quickly). Aside from childbirth, there are 2 ways of gaining family members:
1. Bribing other faction family members.
2. Use a stack of troops without a family member to win a lot of battles. The "Captain" gets adopted once he gains some stars.