We've had battery operated toys go off by themselves in the past. I'm pretty sensitive but it's always come down to dodgy wiring.

Re the coloured lamp - DD had one of these for a while until we worked out she was really frightened by it. It had me freaked out for a while because she keep saying the bed was moving - but then we realised that because the colour change mechanism moved, it meant the shadows from the lamp also moved. We replaced the lamp with a non coloured non moving one, and she was happy after that.