Usage of "just", "only" and word-order [intended meaning]

Solution 1:

Only in 1996, Ford sold a rebadged Mazda 626 GV over here as its rebranded Japanese mid-size stationwagon. (1996 was the only year)

Not exactly. More precise meaning would be Until 1996 Ford did not sell a...

In 1996, only Ford sold a rebadged Mazda 626 GV over here as its rebranded Japanese mid-size stationwagon. (Ford was the only manufacturer)

Correct.

In 1996, Ford sold only a rebadged Mazda 626 GV over here as its rebranded Japanese mid-size stationwagon (i.e. it was the only rebranded Japanese stationwagon from Ford)

No. The rebadged Mazda was all he ever sold that year (poor Mr.Ford...)

In 1996, Ford sold a rebadged Mazda 626 GV over here as its only rebranded Japanese mid-size stationwagon (there were no others, I assume?)

Here it's exactly what you said in your previous example. Mazda 626 GV was the only rebranded Japanese stationwagon from Ford

In 1996, Ford sold a rebadged Mazda 626 GV over here as its rebranded Japanese mid-size stationwagon only (but not as a hatchback or saloon)

Correct.

Just 3 weeks ago, there was a sudden snowfall (3 weeks ago recently?)

More or less.

3 weeks ago, there was just a sudden snowfall (no other natural disaster?)

Correct.

3 weeks ago, just there was a sudden snowfall (no other location)

Correct.

3 weeks ago, there was a just sudden snowfall (?)

The only meaning I can fathom for this usage is Suitable or proper in nature; fitting (and only after consulting the Free Dictionary, my first thought was just in the meaning of honorable/righteous).

Grammatically they all seem fine.