Geeze, Lot of variables and symtoms there dude!
If you want to diagnose this intermittant fault , you are in for a possible long ride!.
It took me 5 weeks to find my bad distributor- I went from believing it was a damp related problem, then a voltage, to a temp. related and my wrench thought it was a Worn valve problem!.
I would suggest trying to rule out certain areas.
Get a good volt meter and load tester and check condition of Battery and Alternator.
Then work your way through each system from start to finish. Electrical (inc. grounds),Ignition system, Fuel, DME, DME harness and sensors.
The list may even go on!.
You may be lucky and find it quickly!. But with all of those symptoms- which may not even be linked! you may need some patience and a lot of help from these helpfull guys (with more experience/knowledge than me).
Hope this helps,
Rgds Ben