Its certainly different to visit Scandinavia for a holiday - as opposed to living there.
I live in Sweden and can't help much with any of your questions: theres a UK government website
here with some useful Danish links. I've heard that the Danes expect you to be proficient in their language - but from
my experience of occasional shopping trips to Copenhagen, they are a lot more cheerful and friendly than the Swedes are
A ferry from UK to Denmark would be the best option - however DFDS ended their ferry services (Harwich-Esbjerg) last year. Another Danish company called regina line did hold out the possibility of commencing a service, but it seems you had to email them to express an interest. Last time I tried to find them on the internet, I got '404 Error - site not found'.
Good luck!