The BW has a mechanical parking pawl, so if you have Drive while Park is selected the shift mechanism must be out-of-adjustment or your parking pawl is broken.
Drive while Neutral is selected, I would also believe is your shift linkage adjustment is out-of whack.
Quite possibly the shift linkage is disconnected from the valve body, internal to the transmission. This would explain all three of your issues.
No Reverse by itself would be caused either by a bad rear clutch or bad read band or both.....or the above disconnected VB linkage. But you say "locked up" when in Reverse, as in Park, correct? This again points to shift linkage issues.
I would drop the pan and investigate AND be sure the shift linkage is not damaged, burned on the exhaust pipe, etc.
Disconnect both ends of the linkage and operate the linkage to see it it operates freely.
Then operate the trans from the outer lever without the linkage attached and see if all the positions are there or not and functioning properly.