I have a german website about vacation rentals. Does anybody knows if it is allowed to link https://outdoors.stackexchange.com or other websites, without any permissions?
If you see a question on this site that you think people who read your website could answer, by all means add a link to it there, along with a sentence like "Can you answer this?" or a short summary of the question. To get the link, use the Share link under the question, that way you may earn a badge like Announcer.
If you see a question with one or more great answers, same thing, but use different text like "wondering how to X? These great question has some wonderful answers that explain how it's done." Again use the share link.
The fact that SE gives out badges for sharing these links is a sure sign they want you to do it.
What not to do: don't write an "article" on your site that is a copy and paste of an answer from here, or otherwise reuse text from this site on your site. Using the subject line of a question is fine, using the whole thing is not.