What is the desired system, and is it not possible to use this system to perform the adjustment process?

The desired system is an Mercator projection. I am not sure I can combine 3D GNSS baselines from WGS84 datum and projection points seeing as the baselines are refering to geocentric coordinate system? I thought I would atleast need to do transformation on the baselines into the system, but I still have the problem with the height. Seeing as the height is not referenced to the elipsoid but rather local orthometric. I have red recently on this matter if I recall correctly that you suggested to only use 2D baselines for such adjustment?

Perhaps, but usually not, because you have to define a uniform datum, and - as far as I understand your explanation - this requirement is probably not fulfilled in your case.

I was thinking of maybe transforming the reference point height into the same WGS84 system as the GNSS baselines and after adjusment to transform it back to my projection with the heights. Ofcourse, the height would be considered elipsoidal but that shouldn't make a difference in the end result?

Best regards.