You first need to understand the operating system. The CETME uses a roller locked delayed blowback operation. It is unlike most other systems. The chamber is fluted to allow hot gasses to blow back along the flutes. This allows the case to float on a cushion of high pressure gasses. This keeps the case from sticking in the chamber. The bolt does not rotate. The round goes straight in and out of the chamber.
Keep in mind this rifle is NOT chambered in .308. It is 7.62 X 51 NATO. .308 ammo will not work properly in the gun. The brass is too thin and will eventually give you separated cases. Get a stuck case puller, you will eventually need one. They are simple, inexpensive and easy to use.
You need to get familiar with some things like "bolt gap", "false gap", "ground bolt" and the "HK slap".
They are not headspaced like most rifles. The bolt gap is measured and can be adjusted with oversize rollers, locking pieces and bolts.
The Monkeys at Century really messed up some builds and did OK on most. Before you get too far into it, you need to know what you are dealing with. We don't normally do this, but I am going to refer you to the CETME specialists at militaryfirearm.com. They have numerous "stickies" that will help you understand the magnitude of your problems. Or, help you understand how to fix a minimal problem.
As far as the finish, it is possible someone simply spray painted the gun. The typical finish is an epoxy paint that should not come off unless you are using some ssort of industrial solvent. If the gun is salvagable, I would consider parkerizing, top coated with Duracoat or Ceracote for a durable finish.
In life, strive to take the high road....It offers a better field of fire.
"Robo is right" Fuzzball