+1 to mcarter. The Santa Fe is not enough to tow that trailer safely. Tow ratings assume there is nothing in the tow vehicle, which is of course not realistic. So, you would be towing a trailer that is already too heavy even before you put any gear or passengers in the Santa Fe.
I don't know what the Santa Fe might be rated for for Europe, but it doesn't matter. The US is not Europe. We have busy freeways with big trucks going 75 mph, high mountains, rough roads, and long distances. Also, if you overload your trailer and have a wreck, you would be considered to be negligent and liable for any damage or injury you caused. Imagine standing up in court and saying "well, what I did would have been OK in Europe". See what I mean?
Get a lighter trailer or a heavier tow vehicle, be safe and make your towing experience safe and pleasant.
As for tow vehicle electrical connections, you will need a brake controller which needs a wire to send power to the trailer brakes. You will also need a 12V supply to the trailer from the TV so you can charge the trailer battery while driving, and run the fridge on 12V as well if you want to be able to do that rather than use propane. That requires a 7 way connector and some new wire runs as well as a brake controller install. You can get an etrailer kit and do that yourself, its not hard, but please do yourself a favor and don't do that in the Santa Fe.