Is it normal to have paranormal dreams?

Is it normal to have paranormal dreams? I stayed at a hotel one time that was supposedly haunted. I couldn't fall asleep properly. When I dozed, I dreamt of a dark haired woman sitting on the bed dressed in Victorian clothes. It wasn't threatening or scary.

Then I sometimes have dreams that come true. Normal every day events but the dream was a duplicate of what actually happened.

I've always been able to pick on weird vibes from people and places. I always thought it was normal. Doesn't everyone have a 6th sense? Some folks more than others?