Whether you are or aren't seeing anyone is not anything that he has to know, none of his business, he's an ex. WTF does he think he is thinking you owe him any kind of accountability about your dating life? he is so far out of line I don't blame you for being angry but you should be more angry at him for being nosy about something like that than about whether he was told such a story.

She's 16 and can't tell if a dream was a dream or not? I'd be kind of concerned about that also. That's kind of old to have a hard time with dream vs reality discernment.

First I would tell him it wouldn't be any of his business if you were seeing someone and that he has no right to know either way. leave that at that.

Then I would tell your daughter it's not her place to reveal information to him about your love life but yours and yours alone unless you tell her otherwise.