Is it within the regulations to fit a door closer to a outward fire exit door which has an internal single latch push pad and an external mechanical keypad codelock?

If this is a final exit door I see no problems with this arrangement, moreover if you need security from the outside then the self closer is required to achieve that. The means of escape from the premises is from the inside to the outside, through this door and using the push pad means you do not require the use of a key.

Can a fire exit door be spring loaded ?

I cannot see why not, providing it doesn't interfere with the door opening to its fullest extent.