Hi Stig,
I hope you're having a pleasant time in Munich.
The dates for the Halberstadt School are here :
http://www.frontflieger.de/2-fshalberstadt.html and are given as 19.09.14 to the end of the war.Whereas, according to Jack Herris in AEG Aircraft of WW.I P.4 the AEG School which I referenced with regard to B.I B.100/17 had to be closed in 1917. So clearly operating dates varied according to circumstances for the company run schools. What I believe we can say is that company schools of the larger manufacturers did not close when military FEAs opened. There was no such link. Indeed the first five FEA's actually existed prior to the Halberstadt school opening given the dates for Halberstadt already quoted.
With regard to ooperating aircraft types other than those manufactured by Halberstadt, that doesn't seem unusual for any of the Flying Schools, but in the case of Halberstadt, although not all Bestellnummer for Halberstadt B types are known the number of trainer aircraft produced by Halberstadt would appear to be too low to equip the school on their own and many Halberstadt B machines seem to have been operated by the Army in any event. A more interesting question would be whether some of the larger already established manufacturers used machines from other manufacturers.
Also while looking up info for the Bavarian LVG B.I in the appropriate thread, I note that there is a photo and colour illustration of LVG B.I No.14 of the Herzog Karl Friedrich Fliegerschule at Gotha (FEA 3) in LVG Aircraft of WW.I Vol.1 which shows a line under the o of No rather, as would appear to be the case with the machines with numbers in this thread. So it appears possible to say following Jean's helful info about Hagenau that the aircraft shown are from FEA 3.
Regards,
Clint