1. Sounds like your reset bar is not going high enough.
Possible issues:
a. The adjustment moved (not real likely)
b. The electrical pulse is too slow. (Check motor 2C, and the S and E relays) refer to the bottom under the transformer on your schematic.
c. The coil stop is broken off in the sleeve
d. Dirty, sluggish plunger.
e. Other mechanical issue
f. Target bank misadjusted with respect to rubber band on the field, causing interference.

For 2. Check your carryover switch on your score reel.

Nothing opening a path to cause chime or reels. Things are CLOSING to complete the path.

In the case of your score reels. If they are working properly, when you score a hundred, the hundreds wheel is activated by the M relay (follow along on your schematic). The M relay has 4 type "A" contacts. You see this under the relay list on the left. One of these completes the circuit to the score reel and another completes the circuit to the chime.

Additionally, when you get to 9 on the hundreds reel, one of the switches on the score reel closes (just to the right of the L (thousands) relay on your schematic). This is often called the decade switch or carry over switch or something similar. Then, the next time the M relay closes, it advances the hundreds score reel to 0 and activates the L relay. The L relay, in turn activates the 1000s reel AND the chime.

In your case, it seems like the carry over switch on the hundreds relay is misadjusted and causing the 100s to carry over to the 1000s when it shouldn't.

Nothing certain, but a few things might work and one will work for sure
1. Penetrating oil on the remains of the screw.
2. Heat on the crank arm. Mini torch, soldering iron, lighter.
3. Then Vise Grip on the stub.

or try to cut a slot in it and see if you can screw it out. (this won't work, but somebody may suggest it.)

Sure fire solution:

Sawsall/hacksaw through the flipper shaft and buy new parts from PBR.

That's usually how that goes. Join the club.

First things first. Get the proper tool for the job:
http://www.pinwiki.com/wiki/index.php?title=EM_Repair#Electrical_short_troubleshooting_Fuse_helper

If you really get stuck, start chunking out the circuit.

Think about when it happens. Sometimes? All the time? Certain actuators?

Generally, right after the circuit breaker, your eyes are your best tool to find the short.

You could disable the R relay and see if it makes a difference. This would cut the 25v circuit about in half.