ayjayef

If you go to the "legacy" page the release note links for the G4+ are working correctly (https://www.linkecu.com/software-support/pc-link-downloads/pc-link-legacy-software/)  Only the last 3 versions have release notes attached though, it was all done in the help file prior to that.

Yep thats the one

The MAP sensor is only indicating pressure on one side of the butterfly though - My thinking is since these have a crankshaft driven supercharger and RPM is still high, even with the dump valve open there is likely a large pressure difference inside vs outside the butterfly. 
I have seen a similar but opposite effect when trying to open the throttle.  Some BMW's have butterfly shaft slightly offset from center, so on those if you let them close too much when returning to idle they are sucked shut so hard you cant even move it with a screwdriver or similar.

Yep, looks a bit extreme but it will be a safe starting point.

Good to hear I'm not the only one ever to be confused with that.  Even knowing to imagine another wave in the missing teeth gap makes my brain hurt.  I can see it sometimes.
 
That fixed it!  
Was 245deg and now -119deg offset (after a 4deg timing light adjustment).  Trigger scope during idle looks good and NO TRIGGER ERRORS!
Starts easy now, timing is steady, idle is good.  Now we can actually start tuning.
Thanks for your patience and odd hours troubleshooting!
Log 2018-11-12 9;11;38 pm-idle.llg
Trigger Scope Log 2018-11-12 9;08;33 pm-idle.llg

Good to hear I'm not the only one ever to be confused with that.  Even knowing to imagine another wave in the missing teeth gap makes my brain hurt.  I can see it sometimes.
 
That fixed it!  
Was 245deg and now -119deg offset (after a 4deg timing light adjustment).  Trigger scope during idle looks good and NO TRIGGER ERRORS!
Starts easy now, timing is steady, idle is good.  Now we can actually start tuning.
Thanks for your patience and odd hours troubleshooting!
Log 2018-11-12 9;11;38 pm-idle.llg
Trigger Scope Log 2018-11-12 9;08;33 pm-idle.llg

I can't help with Kiwi4 but I've played around with quite a few ODB2 bluetooth devices in the past including the Kiwi3.
The gotcha with the Kiwi3 is that it used "low energy bluetooth" which isn't compatible with everything (which is why some of the other threads talk about working on this device but not that).  Seems someone in their wisdom took a working bluetooth spec and split it into a few different versions that don't work with each other.  
Cheap ebay Chinese ODB-II devices are hit and miss and I've had a really good one that worked till it randomly stopped. 
Don't know where on the planet you are but in AU/NZ the Jaycar ones work well on everything I've tried them on without lag.
https://www.jaycar.com.au/obd-ii-engine-code-reader-with-bluetooth-technology/p/PP2145
...and they have a good return policy if for some reason it doesn't work on your setup.  They also sell a wireless one that I've not tried but it might suit your setup better if you are using a external GPS or another device on bluetooth at hte same time.
A bit off topic but Race Chrono is a killer app for ODB-II bluetooth.   Race track video with odb-ii data overlay, lots of tracks in there or you can mark-out your own.  You will get best results using a higher frequency external GPS  (10hz) as phones typically use a 1Hz GPS. 
 

Your ignition table is in MGP, and doesnt go into negative. This means your ignition timing at anything non-boosted is effective a single row lookup. I notice it runs pretty minimal vacuum anyway, but you should still have this drop down to at least -30kpa as it seems your engine would use this at idle.
Your fuel table numbers are very small, and your master fuel number is quite large - this doesnt "break" anything as such but it makes it very hard to get any resolution in your fuel table. eg you can only move from 12.0 to 12.1 and this might be quite a jump in injected fuel quantity. Try changing master fuel trim to 0, master fuel to 5, and then select the entire fuel table and type *4 <enter>. this drop your master fuel value to ~1/4 of what it is now, and multiples the table values by 4. The injected quantity will be the same but its easier to work with the fuel table now. 
It looks like the reason it stalls is because it runs too lean. healthy idle is probably 0.9 lambda and 1.1 is probably stall. Post start enrichment is keeping you going to start with, and when it runs out, your engine goes lean and stalls. Try bumping up your master fuel table a little bit (maybe from 5 to 6 once you do the step above) until it can keep running once post start enrich goes to 0. Then once you know what "stable" idle looks like, you can reverse engineer the post start enrichment numbers to stop the idle creeping up at the beginning but this temporary high idle is not your biggest problem right now.

MAP is Manifold Absolute Pressure, so this is pressure in the manifold (after throttle).  Your "boost gauge" most likely either cant read vacuum, or is connected before the throttle. 
 
Yes, idle will typically be around 35-45, over-run maybe as low as 20kpa.  So although the sensor we are talking about here doesnt miss out by much, decent idle and economy is still usually an important consideration for most users.

I had a similar issue when the voltage to the lambda sensor was too low. Check it's getting 12volts.

Just the +14V (pin A5), and one of the main grounds (A34 or A25)

Just pull the 5V wire out of the ECU connector (leaving all other wires connected) and see if the 5V out parameter returns to normal, if it does that suggests there is a short somewhere.  The pins can be extracted quite easily:  https://drive.google.com/open?id=1MnJlNTBhX_ccv40PbVgIi9XTy4HbXEfJ

Yes this would be the best option 

You cant remove the connector off the sensor, it has a laser trimmed calibration resistor inside that is unique to the sensor.  
You could extend the ECU side of the wiring, or something like one of these:
http://dtec.net.au/Lambda Extension Cable - LSU4.9.htm
https://www.ebay.com/itm/LSU4-9-WBO2-Wideband-Sensor-Extension-Cable-5ft-fiberglass-loom-/262585943294