Page 92 of PDF manual is the Lamp Matrix. (2-40 in paper manual)
They share the common Row 2. Are any other lamps in that row out?
If not... trace the Red/Black wire that is common to the two lamps to see where it is probably broken.

In theory, yes.
An opto switch works by interrupting the light beam from the sender to the receiver LEDS. (the receiving LED not getting "light", when the flipper button is press, is what activates the flipper circuit).
So if the Sender LED's solder joint is intermittent, the sender LED goes dark... basically same as the flipper button being pushed. Causing the Receiving LED to activate the circuit.
(that make sense??? LOL)

Personally... I'd also check for a magnetized coil stop. (plunger is sticking to the coil stop after a flip).

The spinner switch on STTNG runs thru the Fliptronics flipper board. You may want to read thru this thread too, might be helpful: https://pinside.com/pinball/forum/topic/sttng-spinner-not-working-eos-errors

Ditto.. you only get the first pass to shoot. On the return, it dribbles the ball out. I always assumed this was normal. (they don't want you taken multiple swings back & forth to line up your shots.)

Check this thread: https://pinside.com/pinball/forum/topic/sttng-issues
Generally, it's the opto board dirty, at the left flipper button.

(semi-related topic... the spinner runs thru the in-used Fliptronics input, in place of that 4th upper left flipper)

If you haven't already, go get the manual from IPDB: https://www.ipdb.org/search.pl?any=star+trek+next&search=Search+Database&searchtype=quick

1. - completely normal.

2. - normally the game "stages" the balls in various trough/VUK areas (and Borg ship?)
Best to go into Test menu, - T.18 Clear Out Balls Test (close coin door to enable voltage for solenoids to eject balls)
Catch the balls as they come out and make sure you indeed have 6 in the machine.

3. - a) there is a single drop target located/hidden in upper-loop.
Page 89 of manual -- #18 is the target.
See page 79 of manual for assy.

b) Page 95 for switch locations. (switch may be showing closed because there's a ball there?)

c) There is no upper-left flipper. F8 is not used, per the switch matrix on page 94. (unless your spinner is not registering, you can ignore F8. But the spinner uses the circuit on the Fliptronics board... so if spinner is not registering points... it may be something deeper.)

I've never looked at my cannon gearboxes... are they MPC / MultiProducts Company, Inc. assemblies?
If so, maybe contact them.
https://www.multiproducts.com/

Or, contact Steve @ ThePinballResource. He does gear/motor repairs. (for MPC) Maybe he has one to sell.

Those appear to be classic Bally/Stern 1970's flippers.
You want Williams...
https://www.pinballlife.com/williams-logo-flipper-bat-and-shaft-assembly-white.html

(don't forget the 3rd flipper too)

As for rubber... that can be personal preference... but size-wise, you want standard 1-1/2" x 1/2" .
https://www.pinballlife.com/flipper-rubber.html

Yep... especially since the pin that feed that flasher is visibly cracked. Reflow them all.

pins (resized).png

Wow... that was weird. My STTNG club pages we're refreshing, so I never saw the dozen or so newer posts, including those whom already answered & the OP's confirmation of fix.

Doh!!