Yes, your US radar detector should work (certainly in the UK) - there may be some issues with illegality, however, which will vary by country.

On the laser point, the detectors I have seen are actually more like jammers - they have 2 little lasers which are normally fitted each side of the front registration plate (in the UK - not sure where you'd put it in the States ). When the detectors pick up an incoming laser (police normally aim at front plate, since it's supposed to be vertical and they get a good signal from it), the counter-lasers fire back a beam of their own, which confuses the police laser, and stops them getting a fix on your speed.
At least, that's the principle. Can't tell you if they work, since I never go over the speed limit (obviously)