Wow, all these stories are so interesting and moving to read! I suppose nobody knows for sure, but I tend to say yes, I believe.
I think I was very psychic as a teenager and I have lost touch with a lot of that now that I have a family and my mind is constatly working and thinking and busy. I remember I always had a very close relationship with one of my Grandfathers, and I feel like he visited me after he passed. It was a few months later, but I had a dream about him. We were all in his house, my parents and my Grandmother were there. At the time I had one daughter, and she was with me, she was a baby and I was holding her. My Grandfather was sitting in the chair he always sat in, but no one else could see him but me. I had always felt I had this understanding that there are things we do not understand, and it was always a given to me growing up that there is some sort of afterlife and we are connected to it. So in my dream it didn't seem all that out of the ordinary that I could see my Grandfather and nobody else could. Without speaking he told me that he'd be around, watching, observing but not interacting or interfering. His exact words, and it gives me chills even now thinking about it, were "I'm just here to observe." I will never forget that. I do feel him, I feel like he's with me, but as he said he's just watching, never interfering. It was one of those dreams where when you woke up the feeling you had in the dream lingered for hours...really days afterwards.
Aside from that I have had other experiences that make me want to say there is definitely something going on we don't yet fully understand. If it's spirits, I don't know, but I know many people have had experiences they cannot explain.