If I build mnt. Rushmore, jail and switch to police state

do you 0% war readiness when at war?

You should have no WW if you have just declared and no units have been lost yet unless you have built up WW from a previous fight.

This is not to say that being at war won't bring unhappyness from the start.

Yes

with Mt. Rushmore and Police State, cities with Jails will have 0 war weariness.

I hate statue of zeus when I don't have it. Fought huge war everyone was starving til I took that city. whoo, i built so many jails after that to make sure I never have so much weariness.