To answer the bridge part, might be whatever supplier Dyna Gakki used when they built the guitar was cutting their Mustang Saddles a little less as deep. You can do one of two things..
1.) raise the bridge and shim the neck, I don't recommend this anymore because the angle of the strings and the neck sometimes gets thrown off and it requires raising the bridge to a height where the strings rub on the back of the bridge and/or intonation screws and it breaks strings.
2.) Lower the tailpiece, which is that bar you describe that the tremolo bar installs into. It uses a 2.5mm allen key, and the flashlight + angled sides just make it look like it's a star bit, but it's actually a regular allen key. The Bridge is 1.5mm through the holes on each side.
As for the stock tuner mounting holes on the headstock, you are right, those are around 7mm. In order to have bolt mount tuners on it (which all locking types I am aware of are) you will need them drilled wider to suit. I had to do this when used some Scahller M6's temporarily in the mid 00's which then lead to me upgrading to Kluson Tone Pro bolt-mount vintage-style tuners with the safe-t posts - best of both worlds IMHO). I find the Tone Pros pretty reliable and have them on my Jag-Stang and Jazzmaster and I do all that crazy dive-bombing and stuff and I have no tuning issues - they also come in a Standard Fender bushing design that the Jag-Stang uses.
If the switches are backwards, a quick, possibly easy fix (assuming the wires are long enough), would be just to unscrew them and swing them around the other way. And yes, that is backwards that the switch next to the neck pickup is controlling the bridge, and vice versa. It's supposed to be intuitive and have the switch match the pickups. If the wires are too short, some re-wiring needs to be done.
