Every time ive ever thought there was a ghost around me, i start to get cold chills, as many people say to experience as well. I think what happens, is when there is a stronger spiritual activity, places tend to drop many degrees. I belive that with your stair being cold, and only one stair represents that you have one spirit in your home, and it chose your staircase for its entry point.
I don't really think this spirit was there to harm you, as you didn't mention anything being done in that manner, other then things being placed in new locations, things dropping onto floors, or tipping on their own. I think that would mean it was just trying to get itself known to you, as you would think it would be pretty hard to get someones attention if you cannot speak, or be clearly seen etc.
Luckly your out of that house, but to bad for your parents, i'd hope that they don't still see things there, but being near to a graveyard kind of invites them to you, as do ouija boards.
I don't think there is just one little boy singing, man in window aaarrr i forgot to mention in the story how did i forget this me, my cousin gemma, and her boyfriend matty were all sitting down stairs matty laid on sofa gemma on another sofa and i was sat on top of a large speaker we used to have, this was summer still all the doors were open this happened just after the pots being moved the living room door was wide open and we were all talking but the conversation was stopped by the sound of foot steps coming down the stairs one by one and softly but enough to be able to hear what was happening the foot steps came down the stairs through the living room out into the kitchen we stayed still in the living room and listened you could hear the washing up being moved around you know plates cuttlery etc!!! and the humbing sound of a woman due to the heat the back door was open now what ever it was went outside coz there is like a manhole drain cover outside but it wobbly and if you stand on it it makes the sound of metal hitting together as it would obviously be metal but she must have gone outside towards the washing line which makes me wonder.
CAN GHOST EVEN SEE US AND DO THEY KNOW IF THERE DEAD???
MORE TO THE POINT WHO SAYS WE NOT THE DEAD ONES AND THERE THE LIVING???