Yes, I can't think of an exception. "I am so tired of school" "Me too" "I ran five kilometres this morning" "Me too" "I have been to France" "me too" etc. etc.

It depends. For example, if someone say " I am exhausted " and you are not, then you don't answer "me too" Basically, if you are in agreement with the full expression, then you can say it. Otherwise, you can say something nice like " sorry to hear you are so exhausted today." , or "hope you get some rest".