There are many 1936 cents that were made from dies that have the broken leg. I don't know of any other year coins that had a broken R.
Yes that is mechanical doubling on the date.
The same hub with the broken R that made this coin is the hub that made the big 1936 DDOs.
On some coins they did one hubbing using the broken hub then did a second hubbing with a non broken hub which is why the doubled die 1936 cents (die 1,2,3) show that broken R on one of the hubbings but not on the other hubbing.
The non doubled die with the broken R:
The doubled die 2 with the non broken R over the broken R:
