I will answer just the first question assuming you are not talking about standalone mode but you feed an input to Casio or feed the Casio to a computer audio interface.
If this, then you experience what is a ground loop, do a Google search you will feel better.
You fight it by feeding everything to the same electrical output or use a ups, or get a ground loop Isolator or use balanced audio feeds, which is a no go for most DP's.
Hope this helps, I have it too as I can't use the same electrical feed as I use ups and there I have only what's critical on outage.
My Casio and my active monitors get electricity from another plug.
To fight it I use a 2 channel balanced/unbalanced visa versa converter.