For how long can a single-engine turboprop safely run the engine at idle?
It's not stressful at all for a turbine engine to run at idle, you could run it until the fuel runs out. The prop is not feathered (in line with the air stream, pitch 90°) but will be at ground fine, in line with the direction of blade turn, pitch angle 0°.

There is usually no way to disconnect a propeller from a single spool turbine engine: if the engine runs, the propeller turns.