They'll turn the antennas in the satellites off when they're not above a region they're servicing. That's both for legal reasons (you are not allowed to use spectrum you haven't licensed) and physical reasons (less energy usage).

In order to access Starlink you'll need a phased-array antenna, so yes, they will know exactly where you are.

A flat box decorated to blend with the shingles it's resting on might be invisible for a long time.

I meant that you are directly communicating with moving satellites, so they can fairly trivially triangulate anyone using the service.

But yes, they will also have your shipping address, as they are producing the ground antennas in-house.

If they look for them