Every country without regular turn over on top seems to devolve to an evil dictatorship over time. Sometimes kings can be forced to give up power, until they become non-evil just for lack of power, but this takes centuries.

There's a large range. Some things, like executive orders, can be instant. Some things, like leaning on congress to do something, might take longer to have measurable results. Some things, like the economy, regularly only affect the next person.

Oddly, the economy one seems to be the one that people vote for, with predictably stupid results. Also for some reason the economy only includes the gasoline refining industry, so make sure to switch careers so you can be a productive member of society!

That depends on how effective they are when truly needed. Firefighters in my town do busy-work 70% of the time. When they are needed, I'm happy we didn't send 70% of them home for the day.