I don't think it was mentioned yet, in UK they have different standard AC wire colors than in US. In general there will be 3 conductors for single phase AC. Live (or Line), Neutral, and Ground. This is Earth Ground, which is not the same as common ground on DC circuits.
USA
L: Black
N: White
G: Green
UK
L: Brown
N: Blue
G: Yellow/Green
Wire gauge for AC cables inside the cab should be between 14 and 18 AWG. Typically 18 is cheaper and still safe so it will be that. If someone custom made a cabinet it could be whatever they had on hand.
Does your monitor require an isolation transformer? Is there one present in the cab? If there's one there I would use it regardless. Having connectors that disconnect is definitely handy, but not necessarily a requirement. The reason I assume it has an iso is those kind of terminal ends look like they could plug directly onto the secondary side of a transformer. Not sure why the ground cable would have that connector though?
If you don't do this stuff often and don't have any of the connectors on hand, a crimping tool, pins, etc... you may just want to hardwire everything together? However, real ops will look down on your work if you pass it on later. If you ever had to remove the monitor to service it in the future... having everything hard wired together makes that difficult.
edit: we went pretty in depth on AC wiring previously in this thread.
https://www.arcade-projects.com/threads/how-to-add-earth-ground.13418/