navigate the corridors of power =?
The corridors of power are the higher levels of government, where the big decisions are made.
To navigate the corridors of power means to know who to speak to in those upper levels to get things done.
pressure-cooker politics = ?
A pressure-cooker is something that cooks through achieving higher pressure than can otherwise be achieved.
As an idiom it means intensely pressurised.
Pressure-cooker politics means politics where the pressure on the people, due to the situation, subject matter, and/or personalities is far higher than normal.
Yes, but also reliable and stable.
It is an adjective from the British currency (the Sterling), which at least historically was seen as an excellent, reliable and stable currency
wide latitude = wide range?
Yes, but in sense that it is wider than would usually be allowed before being deemed unacceptable.
cowed by = frightened by?
Why "cow"? Anything to do with the animal cow?
Cowed means intimidated.
It's possibly derived from the same root as the animal, possibly from the name of the animal itself, in that a cow is, I guess, easily intimated and herded.
Itake on a life of their own = ? risk their own lives?
To take on a life of their own means that something set in motion is no longer be (easily) controlled.
the stakes just went up = getting excited?
No, it means that the risks and rewards have just gone up, that the implications are more significant than previously.
If you are playing poker then there is a difference between playing for just cents compared to playing for hundreds of dollars... the stakes are higher, so there is more pressure, more risk, more reward etc.