I can also tell someone's problems in life, and background story very well after just meeting them, and sometimes, not even properly meeting them. It sure does sound like you are an empath! Welcome into this knowing life Yes, I can always tell when someone is lying, and I have always felt someone watching me.
Now, about your dream first, I believe that this dream was a night time visitor wanting to mess with you. This has happened to me a lot, but stopped after I smudged the house.
A lot of the time, when we feel that someone or something is watching us, or following us, we tend to make it into it is something bad. But it could be your angel or something trying to protect you and watch over you. You could also be feeling left over energies from your past, or someone else's past. I recently got rid of a lot of stuff in my closet, and now it does not feel like something is watching me from over there.
I suggest you invest in some crystals, protection crystals. Google it, there are loads for so many things! Ebay has some really nice ones that are easy on the wallet. Etsy also has some really nice ones too.
Lots of Love,