Is the approach Category defined by the speed at Max Landing Weight or by the ACTUAL weight ? I.e. Is it fixed or does it change according to actual scenario ?
Fixed by certified structural max landing weight (the landing weight when not runway limited).
In the U.S. at least, if you elect to fly the approach at a higher category speed then you are bound by the minimums for that election.
There is one business jet I am aware of (one of the Gulfstream models) that are Category D for straight-in, unless they depart knowing they will land at less then a specified weight. They then activate some certified placard that places them in Category C for that flight.
Denti: the 727 was that way, certified for Category C for straight-in, D for CTL.