First things first. The cam chain is not adjustable, if it's stretched, it needs replacing. However, I don't think this is your problem. It's common on these 3 cylinder engines for the exhaust valves to burn out causing a loss of compression on one or more cylinders, hence the misfire and the plug(s) sooting up due to the incomplete burn of the combustion charge.
I'd suggest getting a compression test, cylinder leakage test and cylinder balance check done first. If any discrepancies are found, the head will need to come off for checking and hopefully, just one or two valves replacing. Worst case scenario is the valve seats being burnt out, but even these can be replaced by a specialist which most garages use as a sub contractor in cases as this.
Get the checks done and some kind of estimate to the total cost of repair before deciding on the cars fate.
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