first things first, it's very bad to run a car with no battery attached to the electrical system. The battery, even if it's dead acts like a voltage regulator, otherwise the alternator can produce ungodly amounts of spiking electricity, with no control to stop it... at least as far as I understand it. You can run a car off the battery w/o an alt hooked up, but dont do it the other way around.
You need to obtain a factory service manual, and do some reading, as well as familiarize yourself with the basic mechanical principles of a rotary.
The mess of wires might be unplugged emissions components... the smoke could be coolant seal o rings, oil seal o rings, or a stuck open Oil metering pump. I heard that this is a common thing with smoking FB's, but it might just be the carbed ones, so do some reading on it.
Also, I'm more of an FC guy, but if you plan to swap in an FC engine, I would recommend doing the entire FC3S front sub-frame swap, which will get you better brakes and suspension options, rack and pinion steering, which is much better, and stock mounting points for an FC 13B engine. I would also recommend to use a megasquirt (or better, ie: haltech, microtech, motec) standalone engine management system if you do a complicated swap like this. It will get rid of a LOT of unnecessary components, extra wiring, and just generally make it a much cleaner process than re wiring a bunch of stock shit.... however it does present the issue of dyno tuning.
Where are you located?
Some good sites for parts are:
mazdatrix.com
atkins rotary
pineapple racing
racing beat
RE-Speed
corksport
check those out.
FSM's are also available online as well, do a search for them on google you will find tons.
I hope this all helps, I'm bored so I decided to be helpful!
Max.