Strange Goings-On

Suddenly in the middle of the night, a loud song sung by an enthusiastic man blasted into the quiet darkness. There was a rustling then it stopped. I patrolled the house with my jaw set in an aggressive thrust. Nobody there; it was the record player starting up all by itself.
A few nights later the smoke alarm went off at about 5 o'clock in the morning. I was convinced that Offsrog One had come in from a party, made some casual toast and burned it. But no, it was the smoke alarm going off on a whim.
And the bathroom extractor has started intermittently screaming like a panicking fox (we have those, too, in the garden).
We think that there are electrical surges that set all these things off; many years ago when the Offsprogs were mere sproglings, we had a strange blue octahedron-shaped toy that played electronic versions of things like Incy Wincy Spider and Humpty Dumpty. It would run through an electronic chromatic scale, settle on a note, and then a bored sounding woman's voice would sing the nursery rhyme deadpan, before the scale ran up or down again and the voice said 'Bye-bye'.
You'd hear it set off on its spooky journey in the wee small hours, a non-existent voice singing to a non-existent child, set off by the fridge switching on its internal refrigeration unit. Permanently insomniac, I would listen in a state of tension from the bedroom downstairs (it was an upside-down house), only relaxing when it said goodbye for the night.
Either that, or we have a ghost. I hope it's a friendly one.