The clutch.
It isn't fully disengaging for whatever reason.
It could be a faulty cable, it could be contaminated clutch parts, it could be physical damage to the clutch parts, but your clutch isn't disengaging when you depress the pedal.
Reverse only grinds on selection when one of the 2 shafts in the trans are spinning.
The output shaft only spins when the car rolls... so if the tires aren't moving then the output shaft isn't either. This means if the car is stopped, it isn't the output shaft.
That only leaves the input shaft, which is controlled solely by the clutch. If the input shaft is spinning, (and we know it is because reverse grinds on selection), then the clutch is at fault.
You're looking for a clutch problem, and that will take care of the reverse grind, as well as the difficulty shifting into the forward gears.
The forward gears use sync rings to match shaft speeds, so they will use friction to fight the dragging clutch until you can select the gear. Reverse has no sync ring, and isn't a syncromesh gear, so you are actually sliding a gear into another gear, and if any one of them aren't completely stopped, you get a grinding noise.
Thus, if reverse grinds and the car isn't in motion, then the clutch is not disengaging for some reason.
