Your white smoke at startup is not too bad. About normal for a cold day. The fact that it lingers is surely due to the fact that it sounds like you're sucking air for the first 1 min after the car starts up. It could be a bad injector, but if that video is from an initial morning start-up, I'd say that you've lost some prime overnight. It really sounds like mis-firing due to air in the lines, rather than a really bad injector.
If the car seems to run fine, but has excessive white smoke upon start-up and deceleration (like coming to a stop, taking off, and then seeing white smoke), then your valve seals are likely bad. They dribble oil into the cylinders, and it builds up overnite, and when the car slows down. It may also explain the oil on the injector, but probably not.
To your oily injector: I've seen that happen sometimes. It can be anything, but what I usually see is a bad valve-cover gasket that runs oil down the front of the head. It will follow the threads of the injector, and collect on the threads and tip of the injector. I've washed the injectors off with brake cleaner, put them back in, run them for a while, and the problem does not reappear.
You oil consumption (about 1/2-1 liter every 5000 km), is about normal for a TD, assuming you're using Dino-oil, since vaporized oil gets sent into the intake thru the PCV valve and gets burned in the compression chambers. If you're running synthetic oil, your consumption should be a bit less (say, closer to 1/2-3/4 liter every 5000km). Nothing out of the ordinary though for an older diesel.
I'd look to the VG gasket. Maybe, run a compression test when you get the pump back to confirm the compression is good on all 4, then pop-test the injectors. Either way, I wouldn't worry about it too much, if the car runs fine otherwise. It really sounds like the missing/smoke is due to air in the lines/pump. It could be possible (as others have already noted) that your return lines are leaking fuel over the #3 injector, its running down the injector, and loosening up the soot/carbon down the threads, etc. This would explain both the goo on the injector, and the loss of prime (i.e. air in the lines), that you car seems to have.
Good luck, and let us know what you figure out.