The baseboards are easiest to place on top of the panel, and then you can fill all the gaps and paint ...
Regarding the skurkloss, buy planed wood, e.g., 15mm if the baseboards are 12, the same there, mount and fill.
If there is an inward slope due to the casing, it doesn’t matter much (a couple of tubes of, e.g., Biltema’s Multibond is recommended as it both glues and seals).
Regarding the corner, you will have to notch a bit against the frame so the baseboard can be finished with a miter like an outer corner ...
Another option is to cut the panel to height, screw a smooth strip under the cut, and mount the baseboard against it, avoiding gaps. The same with the casing, but there, mount a thicker block ...
More work, but easy if you have a circular/plunge saw and guide/rail ...
A multitool is also handy.