Forest Temple
In the Chronicle, do not discard sites with any 
cards.
Q: Does this protect sites from being discarded even if the winner does not rule it?
A: Yes! It will become a ruin later in the Chronicle, though.
Q: Does this protect sites immediately after being built, or only in the next Chronicle?
A: It immediately protects sites.
Q: If a site has a Beast card and an edifice, but the winner does not rule it, does Forest Temple protect it from getting ruined?
A: No. All Forest Temple does is prevent a site discard, not whether an edifice degrades to a ruin from lack of rule.