Is it appropriate to carry furniture with bike and suggestion for equipment
Based on the photos on the Christiana website I think you'll be fine. The exact law I'm not sure of, I can't find a translation of their bike laws online.

 

It seems that people do carry big loads on bikes there, which isn't surprising given the strength of their cycling culture. You have the right idea about not doing it in rush hour.

The generic load carrying questions are easier to answer. I suggest not loading with the centre of gravity as high as your photo because it means you can't ride on roads where there's a side slope, and cornering is harder. But if that's the trailer you have, that's the trailer you'll use. Just be careful.

I would build or modify a trailer that's as wide as I can get down the paths in the area, once you have somewhere to live. I have built trailers more than a metre wide and not had problems, and in both cases I have built them so I can have a flat platform over the wheels, which lets me have loads wider than the trailer easily.

(big) (big)

(same trailer, flipped upside down to use a second set of dropouts. Or just load it so you can have a higher layer of stuff that sticks out more)