wipers- check relays and fuse box, then wiring. If you can, use jumper wires to the main wires on the motor to see if it is ok.
tranny- check the linkage and cable from the column to the transmission. Start there.
not sure what you got on problem 3, but it has a wiring issue...kinda weird it only does it in neutral...
Don't worry about the key thing...carry over from AMC...I owned a J10 pickup that if you left the keys in the ignition, they would fall to the floor and lose em. I could run/start it without keys. The only time you needed the key was when you "locked" the column. Just wiggle your wheel and you'll be safe...lol. My old scrambler did the same thing as my J10.