Tony's spot on but if you're worried about slackening the injector unions with the engine running you could try this. Remove the three pipes between the injector pump & injectors, clean them out, replace pipes, tighten the unions on the pump, tighten the injector unions finger tight, spin the engine until fuel appears, stop cranking & then tighten. When the engine starts keep it running to get up to a good temperature. The grey/white smoke is probably water in the fuel. The alternator light is a totally seperate issue.
Listening to the youtube clip, I don't think you have any mechanical problem. Get the filter/ aglomerator fitted asap and check for water in it regularly.