Ok, here are some of my thoughts/observations.
First, it is clear that you can build something larger from a smaller fabrication unit. A tier 14 Shipyard can build a tier 15 dreadnaught or huge space station.
Second, shipyards are defined by what they can build, warships and capital ships.
To me, it seems logical that with the proper raw materials, blueprints, and starting fabrication bay, one could build progressively larger fabrication units.
So lets say for a moment that we have a carrier which has a fabrication unit onboard which can fabricate small fighter craft. Say tier 9. To me, it makes sense that they might with time and effort fabricate a shipyard that can build warship. However, once it is made, I think it would count against the MBL.
Keeping on with this carrier idea, lets say that they decide not to use their fabricator to build a huge shipyard. Instead, they just decided to make what it was designed to, fighters. That's fine, they add to the small craft section of the MBL.
Thus, with regards to 1, sure, just so long as it can't build a warship.
With regards to 2 I think that a single shipyard could count as a 'major presence' in a system as that is what new factions start out with. That said, I think we must also remember that the number of systems you can have count towards your MBL is capped by the largest number of players you have had. Thus a shipyard visiting a random system if you are at your MBL cap, does't count for the purposes of MBL.
To 3 & 4, I think it is certainly plausable to section off a part of your area and build more then one thing at a time or to have a ship with more then one fabrication area. Consider for a moment a modern 3d printer if you are building two things small enough to not interfere with each outher as it's building, then you can certainly build more then one thing at the same time. However, there is a obvious limitaiton, the print head can only be at one place at a time. Depending on the nature of the fabrication unit, I think other limitations may appear.
To 5, I think shipyards could resize themselves to become as large or small as needed. Consider for a moment a shipyard with an expanding middle section to accomadate larger craft. In terms of what size they should be counted as, to me it seems logical to classify them as the largest that they can be. You shouldn't make tier 15 shipyards because then they would fall under the huge spacestation catagory. However, I currently don't know of a reason that you would have your MBL shipyards be smaller then tier 14 except for flavor.