Can I tow with my 2015 Golf TDI?

You have the hitch, rent a trailer and load it with weight and try out your proposed loads. Sand or dirt is cheap and if you or someone else needs some even better. Drive it around and test it out. Take some out until you are satisfied with the weight. Make your own specs and share. Sounds like $50 and some time should answer your questions.

Wind resistance will mostly just make your fuel economy drop. I assume lowered speeds so that may not be that bad.

Little late, though here are the specs from Top Gear:

At a minimum i'd be looking at getting a trailer wiring with BCM integration, trailer sway control via ABS is just as good at controlling it with the 10% rule.