Ghosts Of My Loved?

My story, starts in 2007, when my 76 year old grandma died. I loved her a lot and missed her. When I got home from her funeral one night, I started to cry, thinking about her. All of a sudden I felt an eerie presence that comforted me. My nan always used to wear this distinctive perfume, it was rose and it was very strong. I have a small room and when that presence came, I could smell the perfume.

My grandma was cremated and we haven't had the chance to spread her ashes yet, so very creepily, my mother has kept them in her wardrobe. Many times, when going to bed my mother's room door is open. I have seen a elderly woman sitting on the bed. When I enter her room, I feel watched and it is quite creepy. My mother isn't the kind that belives in ghosts but she says "If grandma was a ghost, she wouldn't hurt you, so even as a ghost she won't hurt".

Another reason for this post is something I saw.

I have grown up with cats all my life, one was born before me and died when I was quite young. I had 3 cats, one is still alive. A few years ago I let my cat outside, and being pure white, I could see him. About an hour after I saw a pure white cat bolt past me and jump then disappear, my cat was outside and is very furry. This one had a sleek body and short fur, like one of my past cats. I have never seen the cat again but I would like help and explanation please.

Thank you