"나는 너를 믿어요."
Translation:I trust you.
As far as I know, you don't really use 당신 and it could be a bit offending if you do.
당신 is more formal, both are rarely used and 너 is only used with someone you are very familiar with
But im not korean and its been awhile since i studied so you may want ti let someone back me up on that
This is correct. But actually since 단신 is more honorific it ends up beinf kind of rude if used to address someone. Titles are always used instead of names or pronouns.