Does one have to ask (Pilot2)ATC for permission to descend from cruise or is the fact that the flight plan includes a star (with its descent / altitude limitations) adequate? Can one just go down?

My problem (in life, not just ATC!) is that I'm never quite sure what I am meant to do.

ATC will clear you to descend.  With a STAR, if they tell you to descend via the xxxx Star, then you are cleared to follow the STAR vertical and lateral guidance down to the given altitude.

You should get this call either a few minutes before the first STAR waypoint, or if the TOD is before that, you should get descent instructions a little before the TOD.

Dave