Hello & welcome to the site, in answer to your questions...
1. Yes, they are operating normally
2. you'd cut the two wires feeding each coil and insulate the cut ends, & remove the coils from the mech' via two screws (each) on the back of the mech'. But, if they are working as described above, there'd be no reason to remove them.
3. NO... The 12 volt supply mentioned in whichever post your referring to is internal to the coinmechs logic board, so you can't use it to power anything else. Instead I'd splice into the lightup signs 120v supply & use that to power a 12V DC power supply to drive your neon, (or mini cooper, or whatever...
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