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Ahh, brings back memories. I was given an Elan frame to convert for track racing, still one of the best racers I've ever ridden, even if it was makeshift! Paint was as damaged as yours, if not worse, and basically in exactly the same areas. Unsure if just down to use or the finishes on these things weren't the most robust.
I stripped mine down and went for a Holdsworth Pro replica:

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Great little project.
Btw, headset cups and BB left in whilst painted?
http://imageshack.us/a/img30/4858/1gfg.jpg -
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Class. And my stays are waaaaay more rusted than that on my new build. Should I be worried?
Sand the rust down and inspect, a lot of it can sometimes just be removable surface rust (if not stupidly corroded, with holes crumbling open etc etc...), which cleans up pretty well and only really leaves small pitting in the surface. In this state you'll be able to inspect for cracking/structural damage. Clear coat if need be and keep a constant check.
^^seconded re. porn. Very nice frame and will look amazing fully built.
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Hey dude, I really don't want to rain on your parade, and it's great to see someone building up a bike for thmselves, but you're going to have some issues with that Biopace chainring. First off, it's not round, but more of an oval shape, and so you'll never find equal chain tension, which is fairly important especially if you're riding fixed. Also, the design itself was slated after being released as the apex of the oval isn't in the 'dead zone' of the crank rotation, so it ended up being tougher on your knees and no more efficient than a normal ring. Sorry to be the bearer of bad news, but it really isn't useable without a variable tensioner/derailleur.
It seems the cycling God that is Sheldon Brown actually rode fixed on a Biopace chainring with no sufficient troubles...
http://sheldonbrown.com/biopace.html
@Pauly1978: Based on the above link I'd utilise the setup you already have when fully built just to test and to see if it actually does work for you. Could save you a couple of £ if it works rather than dismissing the Biopace and buying a different chain ring without trying it out. Great thread/build.
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That the one? No good pictures of that bike I could find
Then, after a little longer, you get to this stage:
