cj

According to that factory wiring, all the shielding on the crank/cam signal lines connects to the throttle body ground. As per AdamW above you should only connect sheilding to a single source so it looks like you leave this alone as far as ECU connections go. You could disconnect just the sheilding wires from the TB ground and connect it to the ECU's shield ground if you want but make sure its one or the other, and dont disconnect the whole TB ground bolt as its what your ECU uses as its ground connection.
After looking at the diagram a couple of my comments above need changing:
On an AUTO engine the VTA connection is throttle position but on a manual, its just idle and "not idle" as you initially suspected so you will need to run without TPS or replace it with the sensor off an auto (or an aftermarket TPS)
The 12v/14v wiring shows you should use pin 3-7 (+B) as your input to the ECU as this wire runs from the output of the EFI relay. - do NOT use the BATT line as I first suggested. this appears to run directly from a permanent battery feed so I have no idea why it says "EFI relay"on the description. The other +B line on 3-1 isnt even shown in the diagram.
There are also 2x vacuum solenoids marked "VSV boost" and "VSV TB ICV", and something marked boost control. One of "vsv boost" or "boost control" will be your boost control solenoid, but the one marked "boost control - BC" looks to be high side driven from the factory (ie the ecu outputs +12v to trigger it). You probably want this connected to a PWM controlled digital output on the link but these are only available as low side drive (ie they ground the output when active), so you will need to rewire that boost control solenoid so the EFI relay or another relay feeds it 12v constantly, and the ECU grounds the other side to control it. Hopefully you can figure out what these do by looking at what they are physically connected to as I cant tell from the diagram which of the 2x boost related systems is the one you wire up as boost control in the link ecu, or what TB ICV does. You may need to connect one or both of these to get the engine to work correctly but I'm not familar enough with these cars to tell you from the wiring diagram alone.

As Iceman_n says, your VVT config looks a little odd considering the first couple google results suggest these engines have variable cams and not on/off. That being said, your idle fluctuations are not (entirely) caused by this. Only around 1 in 5 idle "cycles" is getting to a high enough RPM to have the cam switching kick in. The majority of your idle issues look to be related to how idle ignition timing is set up. Because your throttle opening at idle is set quite high at around 6%, the idle timing is set quite aggressively to attempt to pull your idle down to the 1100 its being asked for - ie instead of ~15deg at idle like a production car typically has, youre running about 5, and because there is so much air being allowed in by the throttle, when the idle control moves it from 5 to 7 degrees to try bring you idle up 100rpm or so, its overshooting and bumping it up by 300. Then the reverse happens, repeatedly.
You also have closed loop ethrottle control enabled which i've seen cause something similar when not correctly tuned, but it looks like the throttle position barely moves anyway.
To verify this is the problem, try changing closed loop idle ethrottle to open loop idle ethrottle and see if this helps. Next thing is to disable ignition idle control and check again. Expect your idle RPM to jump up quite a lot when doing this as 7% throttle at idle is quite a lot. If this stabilises the idle (but at too high a number), try lowering the numbers in your idle throttle % table until you get idle close to what you want. You may also need to lower the numbers in the top row of your ethrottle target if you get the idle numbers to 0 and its still idling too high.
Once you've got the idle about where you want it in open loop, try turning on closed loop and ignition idle again. You will probably need to adjust the idle ignition numbers a bit so that the 0 error column has roughly the same number as your main ignition table at idle. This may also help your just off idle response too. At the moment its having to jump ignition angle and throttle posistion quite a lot between where it idles and where it needs to be at light throttle
 
FYI this is mostly all in the help files under idle control. Have a read of that section.

That lean condition starts right when your acceleration enrichment stops and the effective injjector pulse width does actually drop a little so it looks like you simply dont have high enough fuel table numbers at that point, or you need your acceleration fuel enrichment to last longer. Your fuel table kind of shows a higher value at 2500-3000rpm which you maybe just need to expand up a few hundred RPM but as Brad says, the whole fuel table is very spiky in general.
You've also got half a dozen knock detections at about the 9 second mark in that log (around 6000 rpm) which your knock control has dealt with, but they look "real" in that with a few degrees of timing pulled the knock stops, then as soon as the knock timer expires half a second later and the timing gets put back, there is another knock detection.
I'm guessing the 80% ethrottle target until 4500 rpm is intentional and maybe for basic traction control? You've also got a 2% minimum ethrottle target at all RPM's which may mean your engine breaking is quite light and revs may even hold a little between gears as your throttle never fully closes. If you drop this to 0% target above say 2500 or 3000rpm you'll still be able to idle but the throttle plate will close completely on decel.

MGP should roughly match your gauge. (MGP = Manifold Gauge Pressure). -21" is -10.3 psi so while its not dead on, its in the same ballpark. Also, -7.4psi MGP sounds like a reasonable number for idle vacuum. When the engine is off, but ECU on, does it read roughly 14.7psi/101kpa? If this checks out, i'd say your MAP sensor is reasonably healthy.
Do any other sensor values jump out at you as wrong? hit f12 and have a look at the various runtime value and if anything looks completely out of line with reality (eg when its cold with ECU on and engine off, most temps will be within 5deg of ambient).
When its running badly with everything plugged in, is your AFR high or low? can you post a log and your pclr please?
 
 

I notice from your first PCLR and log file that you've really only tuned below about 2000rpm, but your test run spends most of its time about 2000rpm where you have compltely untuned 70 values in most cells. Assuming your lambda sensor is set up correctly, then its running very lean (1.2 lambda) for 90% of your log, which explains it running badly. 
There are a few seconds in your log about 1:26 where you're speeding up in a tuned section of the fuel map, and while its not at your target lambda (0.85), you are at least getting a reasonable lambda number (0.95ish).
Try putting sensible guesses into the untuned part of the map, or simply using the mixture map function with a log file to roughly adjust the untuned numbers. If it still runs terribly with a roughly correct fuel map then go looking for other problems.
Have you had a look at the fuel maps in a couple of the modelled fuel base maps? They tend to look roughly flat at 90-110 for the majority of the map above 60-80kpa, drop off to 50-60 below 1500rpm or so, and slope down to 50-60 between 80kpa and 20kpa. There are a few bumps around peak torque, but they dont slope smoothly from 20 up to 100ish like a traditional map does. Google up volumetric efficiency table and have a look at the shape of them for any engine/ecu - even though the numbers may be different than what link uses. I've never tuned a rotary, but if that was a piston engine, I wouldnt expect the <2000rpm fuel table to be far off what you've go so far, so dont actually see a problem with the ~80-90 values you've got in there. Remember, this isnt directly a "how much fuel do I use" number in modelled, its a "how efficient is the engine running vs its theoretical maximum at this amount of engine load" number. so another part of the equation in the background already deals with the fact that you need more fuel at 200kpa at 6000rpm than you do at 110kpa at 3000rpm, these numbers may both be say 105 on a finished fuel map.