Boarding with engines running

Is it safe/advisable to board a small single- or twin-engined aircraft while
the prop(s) and engine(s) are turning? I'm just wondering if this is feasible
if you just have someone getting on or getting off (with the pilot being in
the aircraft the whole time).

On a related note, how long can you safely leave an aircraft (engines off)
with just the parking brake set, and when do you normally put chocks under the
wheels?

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