hi johan,
i wonder if you can click on "engelska (usa)" , and then change the language as below. please also mark the “don’t check spelling” box. based on my test, it can resolve two situations you mentioned (but there is no such an option to disable the spell check function for all word document in office 365, and thanks for your understanding). will you give it a shot?
 
besides, as our forum focuses on office 365 for business online services, it is suggested you post these office online questions in ms dedicated office online forum. to post a new thread there, click participate>ask a question.
answers.microsoft.com/.../officeonline-word_online
thanks,
april