Yes, turning the prop by hand before starting can have all the above advantages and is something I like to do. With anything that has one or more inverted cylinder (radials, Gipsy Major etc), I consider it a must-do every time, but with a flat-engined aeroplane that I know well or have flown the same day, I'd probably not bother unless I had some good reason to. With Gipsy it is easy to treat it as if the prop were live, you just pull it through as if you were hand-swinging the engine. With a big radial, especially with a 3 blade prop, you have to think a bit harder to keep yourself out of danger if the engine fires. Make sure you are standing in the right place, on firm footings, no loose clothing etc, and with the momentum of your body movement carrying you away from, not into, the prop arc. And keep your senses really tuned in so that you are ready for the slightest chuff (which might make the prop move smartly in either direction) Really really treat it as if it will fire, don't just think iof it as a hypothetical. Obviously check switches off, throttle closed, chocks / brakes set and any other checks applicable to type.
I would not myself turn a prop BACKWARDS except if the POH told me to, and then only with a degree of reluctance and a proper understanding why I was supposed to be doing it. Some engine ancillaries may not take kindly to it, nor may reduction gearing on some engines, and on radials without inlet manifold drains it has been known to make oil in the cylinders disappear into the inlet manifolds, only to be sucked back into the combusion chambers upon startup. This can lead to a partial or complete hydraulic lock, with possible bent con rod and subsequent engine failure sooner or later.