When a seller delivers a car - that's usually a bad sign that something's not quite right!
However, there isn't much of what you've said that indicates the car is in to bad a condition. I wouldn't worry at this stage about it. Services should be done at intervals that doesn't let the engine get in to bad a condition, so when you service it, the car/engine shouldn't feel that much 'better'. However, if it hasn't had a good service in a while, a good service can make a heap of difference to how a car runs and feels.
Before you didn't push the dipstick back in all the way oil wasn't flying around the engine bay, and the TD4 has a number of ways of creating this particular phenomenon. As said, you may have cleaned the oil up - but you won't have cleaned it all up, there will be stuff in nooks and cranies that will seep down for a while and disperse in normal use. I don't think you have mentioned taking the under tray off (a cover that bolts under the whole engine) so I presume it is missing from your car - together with the 2 side plastic panels. These can stop some of that oil leaving marks where you park - although my L Series diesel still manages to create sizable markings
So get those filters on and oil in the car and see how it goes. See if the smoking stops, if not, that's a separate thread to see what's going on.
Incidentally, that spec sheet for your service kit says 10L of oil, my L Series only takes a smidge over 4L when I service it. The sump on a TD4 must almost be the same size and the fuel tank if it needs all that!