OK, so the rad has some furry bits and bobs sticking in the finning which will probably just wash out easily using a hose from back to front. Never use a hose with any pressure or a pressure washer from the front to the back as this will simply drive the crud further into the finning.
You need to use a flashlight and a mirror and get behind the rad to see how much of the finning is clogged, it's difficult to see this from the pics. The worst areas are normally the bottom outer corners.
Karcher sell a 90° swivel head for their pressure washer wands and this is great for getting in behind the rad and washing the crud through from back to the front.
Generally, the principle should be lots and lots of soaking, leaving the water to soften everything followed by some general washing through. Rinse and repeat. Lots.
Engine paint peeling is to be expected on almost any K at the age of your bike assuming it has been used in the winter months. Brian