Is voltage on the ground conductor a sign of short circuit?
I am not sure where you live, but I have never seen that particular type of conductor connector. In answer to your first question you probably don't have a short circuit. If you did you wold have your overcurrent protection tripping or blowing if it was a fuse.

In answer to your last question, yes you have a problem with the splices. I appears they are not making a good mechanical or electrical connection. This is causing a fluctuation in your normal current flow. From what I can see is that your splices are failing. You need to go through you residence and clean and  replace as many of these as you can find. I would use a standard wire nut.