Even if they don’t, they can use trilateration/triangulation (for which I assume they always have the necessary information: signal strength and approximate distance) to pinpoint the exact location.

Good question. Big picture, the phone companies have access to that information any time they want.

The E911 laws, though, only require that the location information be obtained and forwarded when the call is placed.

So, I don't know. I don't know anything beyond that.