Hi Drop!
When cleared a STAR, you can descend to the altitudes given on that STAR, unless ATC has given you other instructions. I frequently get "cleared xxxxx B arrival, maintain FL so and so until xxxxx. Then you may fly the given track, but maintain alt until point xxxxx, or sometimes until ATC gives you a lower alt. This is sometimes a bit confusing.
Are you also cleared for approach when cleared a STAR? This is a tricky one, as the rules vary from airport to airport. A clearance to fly a STAR will at some airports also mean that you are cleared approach. At other airports you must enter the hold where the STAR terminates, unless given a specific approach clearence. Ask!
The controller is responsible for adequate terrain separation when vectoring, but the ultimate responsibility rests with the commander. ATC will NOT correct for wind, temp or QNH, and you must reject any clearance to altitudes below your corrected minimum altitude. Some controllers have no idea what corrections you are talking about.