Couple of questions

[Atilius]

1) Is there a condition that would let me test the (net) population growth rate in a settlement? (There's one for tax level and one for health)

No.

2) Can what advice is offered be modded? I know the messages for a particular advice trigger can be modded, and custom messages & advice can be created, but not if we can mod the game so the condition AdviseBuild is set differently.

You would need to modify the advice trigger.

3) What does a general have to do in order for the NoActionThisTurn condition to be false?

Not sure. Definitely can't move. Don't know if construction of a building or unit counts.

4) Is there a way to change/set which building can and cannot be destroyed?

Partial answer: Any building name prefixed with "hinterland_" is indestructible. Government buildings (core_buildings) are also indestructible, but there's no way to mod this.