K7000 grounding and wall socket mod

[Tithis]

I've been rebuilding a 25" k7193 monitor and just finished a cap and flyback kit along with reflowing suspect joints and joints going to connectors. Before I put the chassis back in the frame and hook it up I have a few questions.

Am I correct in that the chassis doesn't connect to the frame of the monitor electrically in any way besides the black dag wire?

I want to modify the monitor and isolation transformer to plug into a regular wall socket. I'd imagine the live and neutral wire from the plug would go right to the input of the isolation transformer. How about the earth prong? Both the monitor frame and and isolation transformer have a green earth wire. Do I just splice these together and feed them to the plugs earth prong?