OK, here's the brakdown: what I think you guys mean is the Volkswagen Voyage, a.k.a. Volkswagen Fox in the U.S. market. At least that's what I'm seeing in most of the photos.
Brazilian project from 1981. In fact, it's the notchback version of the 1980s Volkswagen Gol.
It was sold in the US as the 'Fox' from 1986 to 1992 with a sedated version of the 1.8-litre AP-800 engine. This unit produced 90bhp (petrol) or 96bhp (alcohol) in Brazil, but only 80bhp in the US-market car. It was a simple matter of tuning (and fitting a catalytic converter) - the Fox should not compete with the Jetta after all.
4-speed manual 'boxes for States, alright, but only for 1986-1988 I think. Our cars had 5-speed manuals, except the early-80s lower models.
There are MANY legends surrounding the origins of the so-called "BX family" of cars, made up of the VW Gol/Voyage/Parati (Estate version)/Saveiro (small pick-up).
Some legends claim it's a Brazilian design based on an Audi project for a small car which was dropped in favour of the Audi 50 / original Polo. Proponents of this 'theory' point to the fact that the Gol (developed in the late 70s and released in early 1980) had a longitunal engine, a configuration favoured by Audi over VW's transverse-engine approach to front-engined cars. (note: remember that the 1970s and 1980s Passats were Audis underneath, whereas the Golf was a true VW).
This is the "German" current (from their claim that the Gol was a half-finished German design that the Brazilian arm of VW picked up and finished by itself).
In fact, there are many points in te original BX family that could point to an Audio origin, not just engine configuration: the AP engines and gearboxes that have equipped these cars from the mid-1980s are Audi 80 engines (1.6, 1.8 and later 2 litre variants); the suspension set-up also has some very Audi-like features - or so I am told.
There is another current though, which claims that BX was an all-Brazilian design. In fact, VW do Brasil made some very interesting (and odd) cars in the late 60s and early 70s, and could certainly have developed this car on its own. Plus, 1980 and 1981 Gols had air-cooled engines (which were dropped soon after in favour of the water-cooled 1.5 and 1.6 litre "short con-rod" VW engine) and several other VW traits.
It wasn't until 1984-1985 that Gols and Voyages received the "long con-rod" (and therefore smoother) AP-600 (1.6) and AP-800 (1.

engines of Audi lineage.
I have been entertaining the idea of buying a 1980s Voyage and fitting it with a late AP-1600 (not to be confused with the 80s' AP-600) since these cars are "modular" and simple to maintain on a DIY basis. Parts are very cheap and available everywhere (the Gol has been the best-selling car in Brazil since 1987, though since 1993 we've had a new model codenamed AB-9. AB-9 and its facelifts have been the best-sellers in Brazil, Argentina, Mexico and are now popular in China, where they're made from Brazilian CKD kits).
Back to the Voyage, it's a nice car. I'm surprised there a 'Fox' in the UK. I know some Voyages were exported to parts of Europe and Latin America as the VW 'Amazon'. Some units survive in Portugal and in northern Africa.
I'm gathering some photos and will post them later. In fact, these things are so common over here that all I need to do is go downstairs and take some street shots. Chances are there will be at least one BX car parked somewhere, and it might as well be a Voyage/Fox/Amazon!
Cheers (and sorry about the looooooooooooong post, but BX VWs are among my favourite car-related subjects!)