Using a mix of ATF is an old trick that was made popular by the Datsun racing teams. I've been using it for years with success. As the synchros get gummed up with crud, they stop working. The ATF cleans them out and allows them to start doing their job again.
Can't get into reverse: Yes, this is because there is no synchro for reverse. The recommended method for shifting into reverse is:
Put the clutch in
Move shift lever into 1st gear
Move shift lever into reverse gear
Release clutch
Hope this helps.