Am I safe working with a power supplier of 12 DC connected to the AC wall socket main line?
It is possible to electrocute yourself with 12V DC, but you have to try really hard (such as poking electrodes into yourself).  Anything below about 50V is generally considered safe to touch.

If the power supply is faulty, anything could happen.  Any decent DC power supply should provide total isolation from the mains supply.  If it's a cheap one of doubtful origin, then it's anybody's guess how safe it is.