1992 Mitsubishi Lancer GSR,1.8 Dohc Turbo, CD5A chassis,4g93t engine,5spd

Question edited for clarity.
Question moved to model category.

Diagram and details in the link.

https://www.google.com/search?q=2012+mitsubishi+lancer.+coolant+sensor+location

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Is it a import? if yes it will most likely have a smaller battery Which you can buy at local autospare shop

if one of the plugs is fouled neither plug will fire

I'm not too sure if those are setup like the Eclipse turbo engines, but those cars came stock with a BCS(boost control solenoid). That solenoid maintained the stock boost on those cars. In the eclipses, you would have to leave the electrical part of that solenoid connected, yet remove the vaccuum hoses to install a boost controller.

I really hate hot linking to other URLs, but I think this guide will help you out a lot.

Boost Controller Installation

First you need to check all your fuses with a test light. The 12 volt light switch wire for the ilumimation of your gauges is just a park light feed, the best way to find it is using test light,it can be found in radio plug or park light switch or fuse board.Your check engine light is not so easy ,first I would check the bulb in dash, then you need to make sure of you lose wire tap connections the check engine light needs a feed to it to come on you need to check your aftermarket ecu wiring diagram to see where this is or get hold of a factory one to find it to see if you can manual trip it with test light.

first thing to do is remove spark plugs and if they smell really fuely you will need to change them if that doesnt help you will need to get the microtech tuned for a good coldstart , this depends on if its running stand alone or as a piggy back
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yea sound like turbo problem get rid of it

9.3 is a really dead battery - replace it and check the alternator. I have seen them go bad with no dash indication. As to the oil being black, you may have worn piston rings, and probably need an engine re-build. Worn rings allow the exhaust of the engine contaminate the oil - you should also see increased oil consumption due to the vapors exiting via the PCV valve and being burned in the engine.

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Check your plugs & timing. Full service.