I've got some similar things happening.
The light on my ceiling fan downstairs will suddenly turn on in the middle of the night. The first 2 or 3 times it happened I thought that maybe I just forgot to turn it off. (I always leave 3 lights on in my house at night but that's not one of them.) Then early one morning about 3 months ago I woke up and saw that it was on again. I KNEW that it was off when I went to bed.
Also, Everynight I heard sounds of something hitting the side of my house. I live on a golfcourse and often get hit during the day. I hear those same sounds at 10/11/12 at night. I've looked to see if someone is playing in the dark but noone's there.
As far as the light is concerned, while my first thought was 'intruder' or ghost, my second thought was that perhaps my neighbor has a remote control devise that's on the same frequency as my fan. (I'm in a townhouse so we have a common wall.) Then I heard from the previous owner that the ceiling fan light did that for them, too. He was an electrician and said that it seems to be triggered by power surges - which we get quite frequently here.
As for the sounds outside everynight, nobody knows.
-Aude.