Art Deco Wall Light - 400mm or 500mm

What is the colour temperature? Is the 700mm available in LED?
The LED version is only available in 500mm. The LED has a colour temperature of 3000k.

Would this be suitable for an exterior light by the front door?
Well it is designed to IP44 so would be suffice to water resistant but it is an unusual choice and may require more cleaning that a fixture designed of external use. It would also give quite a lot of light.

Is this light switched on/off with a string/chord?
Regrettably this light is not available with an integrated switch or pull cord.

Can this light be fitted horizontally, above the mirror?
Yes this fittings are suitable for horizontal and vertical mounting.

How deep is the casing before the light shade starts. Need size to compare with mirror frame depth, hope this makes sense. Also does the 400mm light have the same frame depth?
The outer casing below the line of the diffuser is 25mm deep, which is the same for both fittings.

Does this lamp have a switch or is it operated from room switch?
This luminaire does not have an integral switch and will need to be wired into your main lighting circuit or onto an independent wall switched circuit.