The pickup split pot is probably just wired upside down. In other words, when you push it down, that's when it's grounding out one coil. That can be fixed by simply taking the outside wire on that switch and moving it to the other side. Like lets say the middle lug of the switch is ground, and the top lug is the two coil junction wires. Move those to the bottom lug instead. The trem deal is a reality. There are things you can do to improve your situation like getting new Ibanez studs and installing them properly, and then filing/sharpening the Lo-Trs knife edges. But it's temporary because the Lo-Trs alloys are soft and weak, so they won't hold an edge for very long. That's just a condition of the bridge. Replacing it with an Edge or Lo-Pro Edge, or an Original Floyd or Schaller Floyd would be an improvement (with good studs) and most of those require some routing or at least sanding away at the cavity to accept the baseplate of the new trem. There are lots of threads and tutorials here on this site that discuss this, I'd say start searching and ALL your questions will be answered.