In the old days, the advice on this would have probably have been to have the fuel injectors cleaned. But these days, the modern diesel is a much more complex and sophisticated thing, and black smoke from the tailpipe could be any number of things to do with the fuel system.

You may find the injectors are, indeed, the problem, but you need to check the condition of the pump, filters, EGR valve and even the turbocharger and its plumbing. Something as simple as a split in the plastic turbocharger piping can lead to excess black smoke.

IT SHOULDN'T happen, but there is clearly a problem with the tensioner, which has allowed the chain to slacken and eventually break. When a chain breaks it often results in serious damage to the engine, and I'm not surprised it cost so much to repair. I reckon Ford treated you badly by simply paying for the tensioner kit when they should in my mind have paid for most, if not all, of the repair costs. Go direct to Ford and request they reimburse you.