Are small children able to experience paranormal spirts?

[Sara]

While I was at work, my husband called me and told me that our daughter was in her room talking and he thought she was just talking to her toys. Then she got into the living room even though there was a baby gate set up in front of her bedroom door that was taller than her and she has no way of climbing it. After wards, she somehow got a hold of a marker that was in the living room while my husband was in the living room and she was still in her bedroom and drew strange pictures on the walls that i have never seen her draw before. Then my husband heard the Dora the Explorer "We did it" doll that sings and dances outside but it has been in my daughters room since Christmas and the doll was singing and dancing on its own and the power switch was off! Lastly, I have a picture of my family with my grandmother before she passed 5 days prior to Christmas 2010 and it somehow wound up on my bed in my bedroom with my grandmothers jewelry that was given to me sitting on top of the picture. but the jewelry was hidden from everyone and the picture has been hanging on the wall in our living room. Could this be my grandmother and is my daughter able to see her spirit? Please answer soon...and please don't be sarcastic or rude. Im very concerned on what may be happening.