could you please explain me the meaning of the "用心して" in the following sentence:
親しくする者は特に用心して選ばなければなりません
So, to break down: who/what you become close with, be especially careful and, you must choose.
Does noun + ~te form make up an adverbial phrase or something? Cause it would make sense "who/what you become close with carefully you must choose". You must choose carefully.
Yes, you got the meaning of the sentence right.
Here, the ~て form indicates the method in which something is done. This usage of ~て is not restricted to just "noun + して", though.