Daihatsu earned a reputation for ruggedness and reliability in the 1960s with its light trucks, and built on its good name with a range of small passenger cars and light four-wheel drives such as the Charade hatch and Rocky 4WD over the next few decades. Toyota gained control of the company in 1988, and in 2000 the Japanese company's Australian operation was absorbed by Toyota, and sales ceased here in 2005.
Your list of potential causes is a pretty sharp one and one that suggests you know a bit about how engines work. And it remains that all those possibilities could be the root cause of your problem.
If petrol is getting into the sump, it’s going to be past the piston rings, which means you either have a leaky component in the fuel system (that’s dribbling fuel into the engine when it’s not running) or, as you suggest, something like a dud temperature sensor which is creating a too-rich mixture that is not burning completely and contaminating the engine oil in the process.
Having the car scanned might throw up a fault code that coincides with one of these components, and that would be a very good place to start. But don’t rule out the really basic stuff, too, like a worn out engine or a broken piston ring that is allowing fuel to enter the sump. Or perhaps the car is used exclusively for short trips where the constantly cold operating temperature is leading to an equally chronic rich-mixture state.
Meantime, you’re right to not drive the vehicle until this is fixed as the thinned oil now in the sump can’t protect the engine as well as it needs to, leading to accelerated engine wear.
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It seems pretty clear from these symptoms that the engine is massively overheating. That explains the boiling water in the overflow tank which will be dirty mainly form rusty deposits within the engine’s cooling system. The question then becomes what’s causing the overheating.
There are lots of reasons for an engine to overheat, including low coolant level, a blocked radiator, collapsed radiator hose, failed head gasket, incorrect ignition timing, poor fuel mixture, a damaged or missing fan shroud, slipping fan belt, worn water pump and many, many more. But a good mechanic should be able to assess the situation, do a few quick tests and determine the root cause of the overheating, then you can move forward on a fix, knowing that you’re tackling the correct issue.
The other piece of advice is to not drive the car until it’s fixed. Continuing to drive with an overheating engine is a great way to destroy the engine completely. At that point you need a new engine or a new car.
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If the engine mounts are indeed in good condition (and it can be hard to tell just by looking) then you might be looking at a problem with the idle speed settings. Engines typically idle more slowly when they’re cold and in gear and there’s usually a compensation for this. In an electronically controlled engine like the Sirion’s, this idle-up function will be a job for the onboard computer. But if the computer has lost the plot or isn’t getting the right signal from, say, a temperature sensor, then it can’t bump the idle up a fraction when it needs to. And then, once warmed up, the engine seems normal.
A cold engine that spits a little water out the tailpipe is completely normal. Water is one of the by-products of the combustion process. It’s black because it mixes with soot in the exhaust system. But we only see it when the engine is cold, as once warmed up, the exhaust system turns the water to steam and we don’t see it. A black exhaust in a modern car that runs on ULP is completely normal also.
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