OBT Forum

Lots?

No, many.

Practically infinite, really, because it depends on how you want to define "Star League Defense Force Facility."  While major shipyards and Castles Brian are obvious, there were almost certainly dozens of variations of each.  We know there were something like 500 "shipyards" or "naval bases," which could include anything from remote refueling stations with little but fuel tanks and extra ammo to, well, the Titan Yards could arguably be considered a "Star League Defense Force Facility." 

There were doubtless equipment repair depots of all stripes, for all sorts of equipment, ranging from backpacks to battlemechs.  We don't really have any reports that whole worlds were given over to this sort of work, so it's more probable that nearly every world with a Star League garrison had some sort of repair depot on the grounds of the base, or nearby.  Possibly each Corps had its own set of depots for this sort of work, in addition to the maintenance battalions of the various brigades and divisions themselves. 

Then there would be the weapons proving grounds and test facilities; most of these would likely be in the Hegemony itself, to keep the prying eyes of the Houses away from the classified SLDF tech (though a good case could also be made for locating these sorts of bases in the periphery for the same reason). 

Was the astronomy base at Niops a "Star League Defense Force Facility"?  The initial writeups would suggest it was a pure science job, but later descriptions of the station there suggest that they had the plans for the super-secret Nighthawk PA(L) suits, which suggests that the astronomy facility could have been a cover for a SLDF R&D establishment, making it just another type of "Star League Defense Force Facility."

I seriously doubt the number of "types" can be definitively categorized.  Which gives people all sorts of room to dream up their own stuff.

That's one of the problems with the fiction, especially stuff like this from the earliest books.  "Field Library" doesn't make a lot of sense at first glance, unless it was some sort of recreational library for SLDF personnel on a distant station (which Helm may or may not be; YMMV).  On the other hand...the stuff contained in the Helm Memory Core doesn't exactly suggest it was "recreational" data, given all the scientific & medical stuff in it.  If it were designed as a resource for educating SLDF troops in the field, on their off-time (similar to how instructors travel with many US Military units, even on deployment to foreign countries or aboard ship), then one would expect a different name than "field library". 

I'd say this is something to just shrug off and ignore as being before the SLDF and the infrastructure of the Star League were well-formed in the minds of the BT staff.

Helm had a large SLDF arms depot and had been a fleet base.
And for the Memory Core, it was brought there by an officer that wanted to protect knowledge for the future generations (think of Asimov's Foundation).

And Field Library means perhaps that it wasn't in an official library but "on" the field.

there's a nice list of facility types in the Reunification War

How long did they take to build it?