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Will a 1 &7/9 coupling fit a 50mm tow ball? Also, the adjustable screw at the top of the coupling should be how tight?

No, a 1 7/8 coupling is smaller than a 50mm towball. On the oppostite side of the coin, while a 50mm coupling would fit over a 1 7/8 ball, they should never be coupled together as the coupling would be loose and run the risk of separating. It is essential that only couplings of the same size are used together.
Many modern couplings have an adjustable coupling (clearly marked with both sizes) in order that the trailer can be towed with either size ball.
Regarding adjustment, it should not be so tight as to bind on the ball, so there should be a small amount of play (there's no measurement of play specified in legislation, but common sense should prevail).
Having said that, not wishing to confuse the issue, but there are some recent European stabilizer couplings which use a specific towball with a longer shank. These couplings are designed to be tight on the ball, but should not be used with a conventional towball.