Good writeup! As a big fan of the Mistborn trilogy/Alloy of Law, I've been planning on writing up mistborns/feruchamists/twinnings for some time.
Anyway, I do have a few nitpicks, but first let me say this: I've never played Pathfinder. I have friends who have talked to me about the differences, and my system mastery of 3.5 is
quite high. However, if there are any PF specific changes that I'm unaware of that invalidate any of my points, I apologize and feel free to correct me.
Moving on, starting from the top:
1) I don't think that 4+ skill points is quite right for this class. While I agree that they shouldn't be skillmonkies, they lack the raw combat or magical skills that low SP characters rely on. I'd bump it up to 6+, just to give them some added versatility.
2) I like the average BAB, but I don't agree with your choice of saves. Giving them only high Fort and a Con SAD class is going to create a
very lopsided set of saves. Also, I agree with giving them evasion, but don't recall ever seeing a class without a high Ref save get it. I would personally give them high Ref/Will.
3) The weapon/armor proficiencies aren't really thematic. In both MB and Alloy, the characters wore or carried metal to affect their movement abilities, and in Alloy, the main character used a weapon that was
entirely made of metal (his gun). Also, your definition is vague. How would a wooden spear with a metal head work? Is it allowed or no? If
any metal is forbidden, you've pretty much condemned them to clubs and( staves.
4) Minor point: You say that there are 4 god metals, but only list 2.
5) Much more importantly, the description for "Burning Metals" is a mess. Most of the basics are there, but they need to be clarified. First, and most important, you don't list a duration. Since you went with a times/day mechanic (which works fine), this is very important. Second, you're going to want to add the word 'day' into the frequency description...right now it just says "useable x times" with no frequency or qualifier.
6) Deserving its own point, you're right about the DC formula, it's a bit erratic. Instead of 10+lvl+Con, I'd suggest 15+1/2lvl+con. That moderates the DC curve and keeps things from swinging quickly into the realm of 'impossible DCs'.
7) A slight thematic point: While I understand not allowing all metals at level 1...the thought of an Allomancer that uses more than 1 metal, but not all of them makes me a bit twitchy.
I'll continue this in another post, as this one's getting a bit long.