There is no set angles for all engines.
For example on my type that uses Honeywell Garrett engines direct shaft.
Ground start is when the props are on the start locks which are fine. If they are not the engine won't get up to speed and you will over temp it.
Ground idle is when your just above going into beta range which you have refered to as reverse.
Max beta is as you say max reverse thrust. Yes some types can reverse and its pretty good fun doing it but it knocks hell out of the props and engines.
Flight idle still has some positive torque on if everything is set up right, but this torque setting will still cause more drag than when the prop is feathured. On my type flight idle is between 6-10% torque and 10% torque simulates feathured. Generally the more experenced the pilot the lower they prefer the flight idle. It allows you to "disk" the props and the lower it is, the more drag they create. Which allows you more scope for dumping energy either off speed or altitude. If the flight idle is set to low you get a thing called Negative Torque System kicking in because the system thinks the engine has failed so it feathures the props and it cycles between fine and feathured which is pretty alarming for the punters.
Feathured as you say is a the low drag setting of the prop.
There are 2 distinct modes of the engine which are governed by engine rpm.
Beta mode or ground mode the power levels control the prop pitch controller and the fuel controller controls rpm.
Flight mode the prop pitch controller controls the rpm and the power levels control the fuel flow.
A free turbine eg PT6 works in a different way so I will leave someone who knows more than me to explain the differences.