What is in my house?

First off I wanted to just say I'm a very skeptical person, I generally don't believe in paranormal activity and I feel that there is always a logical explanation to seemingly paranormal encounters. That being said, I am beginning to wonder if there is something paranormal in my home and if there is what to do get rid of it. It started several weeks ago when I was laying in bed with my kids, all of a sudden I got this ticklish over my neck like someone was leaning over me and every hair on my neck and back stood up, I didnt feel afraid but for some reason stretched my neck out and offered it to what ever i thought was leaning in and i went to sleep. That night I didnt sleep well, I could swear I heard someone walking around in my house off and on, then around 3-4 I awoke to the distinct smell of something cooking on my stove. I stayed in be trying to figure out if I couldve left the stove on but I know I didn't, I tried to go back to sleep but the smell was so strong I finally got up to check and there was nothing. The smell wasnt anywhere else in the house. I went back to sleep and heard the sound of my sons bedroom door closing firmly shut. He was in bed me. I jumped out of bed to go check and there was nothing, the door was still open so I figured I'd been dreaming. I didnt think anything more about this night, I figured I had been dreaming since all of this happened when I was asleep or about to fall asleep, until a few days ago. It was 6 am and all my kids where in my bed again, we were all starting to wake up when I heard the distinct sound of one of them get out of bed and run to my bathroom, I turned to see who had gotten up and all 3 of them were still in bed with me. At that exact moment my 4 year old "Lilly" shot up out of bed and said "Mom, I just saw baby Lilly! She was standing by the bed watching us sleep and when I tried to catch her she ran away!" At this point I began to wonder if there was possibly something strange going on since my daughter reacted to it too, when I asked her what she looked like she said baby lilly looks like her. I didnt mention it to her again, I havent felt a strong sense of fear or dread in my home or anything, Im just a little creeped out. Last night my daughter told me baby Lilly kept tryign to get her to talk to her but she was trying to sleep and didnt answer. She said baby Lilly was trying to get in bed with us but there was no room. I asked my daughter where Lilly had been and she pointed to the edge of the bed right where my head was. I looked it up today and I'm wondering if it's possible that this is a mimic? If so how do I get rid of it? If any of this is real I dont like that its interacting with my daughter. Another odd thing (if relevant) is we left the house on errands today and when we got back the heater at been blasted up to 80 degrees, the house was sweltering, I know i didnt do it and my kids have never touched it (and also cant reach). I am aware of all the logical explanations for these occurances, but does any of this seem like it could be a real paranormal encounter, and if so what am i dealing with and how do I get rid of it? Thank you to anyone who has taken the time to read this.