I have had some experiences with what I would call "paranormal", but these two are the most prominent ones I can remember. They're rather vague, but I will explain them the best I can.
I used to live in a trailer home in NC. It was a very new establishment, only about 5-6 years old at the time this takes place. I lived there with my mother, sister, and three brothers. I was about 6-7 years old and slept in the same room with my mom.
I remember one night I suddenly awoke and sat up in bed. The room was pitch black save the light coming from the one window to the right of the bed. I looked around and at first saw nothing. I was about to turn to go back to sleep when I saw it. A full body apparition standing in the bathroom door. It was greyish-white and slightly transparent with no noticeable facial features that I can remember. I sat there staring at it for a few seconds until I finally moved and hid under the covers as quickly a little girl could.
I told my mom about it the next day. She just laughed and said it was probably one of my brothers playing a trick on me. I knew for sure human beings do not look transparent and completely white, but I shrugged it off just like my mom did. I never saw anything else like that again but always felt a certain presence in the house.
Skip a few years and I was about 9 years old. I decided to sleep in the living room with my brother and three dogs. As we were watching TV late at night, we heard heavy footsteps coming from my mom's room and then the water faucet in the kitchen turned on. (The house was one, long building with the the kitchen and living room in the middle. One room and a bathroom on the living room side, a long hallway with an exit to the back yard and the master bedroom at the end on the kitchen side.) The only other person there was, of course, my mom. My other brothers and sister were in their room on the other side of the house. We, of course, got scared. Especially me since the couch I was laying on had a partial view of the kitchen and I saw nothing. We went to sleep and asked our mom about it in the morning. She, like always, shrugged it off and we both never talked about it.
We have since then moved.
Your first experience might be a random paranormal sighting but can't be sure because of absence of further input.
The second one also couldn't be so sure. Because if you have heard footsteps coming from your mom's room, it's for her to explain and you said that she just shrugged and you left if at that. As far as the faucet in the kitchen turning on, did you go and see if it was actually turned on or not or at least if the place was wet? Again difficult to comment further due to lack of information.
Regards and respects to you.