(2)  Who made the 80mm Biometar lens in Exakta 66 style?
It is stated by some vendors that this version of the Carl Zeiss Jena Biometar was manufactured in the Joseph Schneider factory.  However, evidence is contradictory.
It is true that the design matches that of the Schneider lenses for the Exakta 66.  My lens, which was bought new, also came with a Schneider Kreuznach lens cap. 
However, the lens ring states “Carl Zeiss Jena”.

I am also grateful to Donggil Lee of Seoul, South Korea for drawing my attention to the fact that the colours of the Multi Coating on this version of the Biometar “are more like those of M42 Carl Zeiss Jena lenses than those of Schneider lenses including Schneider Exakta 80mm lens and Xenotar 80mm lens”.  I have checked with my examples of these lenses, and can confirm these differences:  the Xenotar and Exakta 80mm lenses have a deeper purple in the multi-coating, while the Biometar has a lighter, pinker colour, although this is not at all like the amber colour multi-coating on the 80mm MC Biometar that came with one of my Pentacon Sixes (unequivocally from East Germany) in the mid 1980s.

There is another interesting fact that does seem to point conclusively to this lens not having been manufactured by Joseph Schneider: the serial number.  In January 2006 I came across a database of serial numbers for Joseph Schneider lenses.  It can be seen at http://www.schneiderkreuznach.com/service/serie.htm, part of Schneider Kreuznach’s own website, and therefore presumably authoritative.
This website shows that all Schneider lenses manufactured between October 1983 and January 2002 (the latest month for which they give data) have numbers in the 14 millions, i.e., 14 xxx xxx, where the x’s = other numerals.  I can confirm that all my Schneider lenses manufactured for the Exakta 66 have serial numbers in the 14 millions (and some other Schneider lenses that I have for other equipment have serial numbers that tally very well with the periods when I bought them).

But my Biometar “III” has a five digit serial number beginning with 48 – i.e., it is in the 48 thousands.  Helmut Thiele’s excellent reference work “Fabrikationsbuch Photooptik II Carl Zeiss Jena” is an authoritative source on Carl Zeiss Jena serial numbers, and it shows that in the last months of the GDR Carl Zeiss Jena manufactured 6,000 80mm Biometar lenses – naturally in the standard Pentacon Six style – and the serial numbers ran from 42001 to 48000.  They were completed on 29th March 1989 and were the very last 80mm Biometars to be produced in the Pentacon Six style.
By the time the Biometar lenses in Exakta 66 style were being manufactured, all sorts of deals were being done between former East German and West German companies, with Carl Zeiss Oberkochen (former West Germany) buying parts  – but not all! – of Carl Zeiss Jena, and Schneider Kreuznach linking up with at least parts of Pentacon.
It is thus clear that the Biometar lenses in Exakta 66 style were manufactured by Carl Zeiss Jena, possibly with serial numbers starting with number 48001.  It seems to me that these lenses were almost certainly manufactured in 1990.

This version of the lens is physically much larger than the original Biometar, with the front extending much further forward and out, to accommodate the standard-size 67mm filter that fits many of the Exakta 66 lenses.  Some users report that in consequence of this, a lens hood (“shade”) is not really necessary with this lens.

(3)  “Exakta” 80mm lens
It appears that this lens was manufactured by Joseph Schneider.  The design matches that of the Schneider lenses for the Exakta 66, and my lens, which was bought new, came with a Schneider Kreuznach lens cap.  Its serial number follows Joseph Schneider conventions used with other lenses for the Exakta 66.  It is in the 14 millions, with a number that would appear to indicate that it was manufactured in January 1991, which sounds about right.  Some sources indicate that this lens is in fact optically a Biometar, but manufactured now by Schneider, with of course their coating and serial numbers.
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The data in the tables above and below are based on published sources.  I do not have examples of all of these lenses (!), and I have not measured or weighed those that I do have.

I note that Pentacon GmbH Foto- und Feinwerktechnik in Dresden has two much newer products that use Joseph Schneider lenses in the Pentacon Six / Exakta 66 mount: their scan 3000 and scan 5000 professional scanners.  The 3000 brochure that they were distributing at Photokina 2002 showed the 60mm Curtagon MF on a scanner.  It’s great seeing these lenses living on into new technology, and an indication of the high quality images that they produce.