What compatible type of paint that can painted over varnished wood?

When you paint over painted stucco you are putting on a second coat.

If you want the paint to stay on the peice of furniture your painting, get some fine sandpaper and rough up your surface first. This will guarentee your paint wont flake off. Hope this helps.

You can use water based or oil based enamel paint, I suggest an oil based paint for projects used outdoors.

yes

No, you should never paint over mold. If it's substantial, you should hire a mold remediation company to remove it, if it's limited, use a 50:50 water to bleach mix to kill the mold, allow the area...