I am on Telegram you can delete a conversation, there should be a pop up and a query asking if you want it deleted for the person whom you are speaking with, if you leave the box unticked it will only delete it for you but the whole conversation will be available for the other person. With all that said, if a person is getting "offended" over a deleted conversation then the problem lies with that person.
Correct, yes. Sometimes my paranoia leads me to delete it for the other person too, just because I get nervous about others keeping receipts on me, but I'm trying to get over this.