I suspect that the 6.5 meters of 1/4" piping submerged in liquid just gives too much pressure drop...... I also suspect that liquid refrigerant is blown through the evaporator before it has the chance to evaporate.
The 1/4" OD tube may not be too bad for 200 watt duty. A superheat reading at the compressor inlet would be in order though.

What must be the minimal speed of the (gaseous) refrigerant in the suction line to ensure sufficient oil return?
Rule of thumb would be something like 700 ft/min on a horizontal run, and 1500 ft/min on a vertical riser. Some may suggest you can live with numbers a bit lower than this.

For a total load of 200W, how large an evaporation surface (copper tubing) do I need? I understand that this depends on the allowable dT between liquid and boiling R134a, but are there guidelines? The lower the dT, the better.
I would seem you're operating at a 10°C TD (-16°C - (-26°C)), which doesn't seem too bad for a bare tube evaporator. First, check the superheat. If it is also at 10°C at these conditions, you should try adding refrigerant