Sttng can be a tricky game....

I believe the issue with the ball lock might be a micro switch on the drop target. The switch tells the game if the target is up or down. I had the same issue with my game.

1) Yes, you need to expose the copper under the screening and solder it to the trace. Use a continuity test to make sure the component reaches the solder pad where that trace leads to.
2) Perhaps, or maybe just some minor adjustment/cleaning is needed.
3) Sounds like switch matrix issues. Go through the switch tests in the diagnostics, see which switches activate other things/more than 1 thing, write it down. Then go through the schematic, trace the faulty switches back within the switch matrix to that wire/pin. Check the voltage on the collector of the pre-driver that is directly connected to that wire/pin (far right pin of a 2n3906 when the flat side is facing you, could be different with another type of transistor) with the machine on. 0v = shorted and needs to be replaced. You can confirm suspicions by measuring the collector on ajacent pre-driver transistors. They should all have a small voltage on the collector pin.
4) This is probably related to the switch matrix issues you're experiencing. All kinds of crazy stuff can happen when a pre-driver in a switch matrix shorts. Game resets, random activation of random switches, etc.

Regarding your flasher issues, check this out. I had the exact same issue sounds like.. I was able to resolve mine. All info in this link:

http://pinside.com/pinball/forum/topic/does-my-sttng-have-a-bad-transformer#post-1083758

#2 - Does your diverter in the backboard work properly and only allow balls into the borg ship when lock is lit?

#3 and #4 sound like opto issues to me. You need to go and test every opto in the test manually and make sure they're CLOSED when not blocked and OPEN when they are blocked. Also, make sure that your diverters on the subway are moving freely and not gunked up. All three of them (2 subway and 1 backboard/ramp) I've had to de-gunk on both STTNGs I've owned...