What is this Gillette?

Very nice indeed! Yes a Gillette Slim Adjustable.

On the underside of the head there will be a letter on one side and a number on the other: the obscured bit of photo four in your picture.
I think I can make out a 4 which means quarter four. Just need the letter and someone will tell you the year, if you're interested.
 
G 4!

So 1961 Q4
 
Awesome stuff, thanks! Does the presentation set mean anything?

Is the 22ct gold normal and is it enduring on this razor?
As far as I know only the Aristocrat versions of the Slim Adjustable had gold plating. The knurling on the handle may be a different pattern, too.

I don't have any experience of the gold plating on those. 22ct is what sovereign coins are made of, as it's harder than 24ct and more precious metal content than 9ct. But it depends how thick the plating is and how it's been used (if it ever has been).