#1
My guitar was used before I got it, but the guy at the store said it was barely used and all that. The nut was like barely cut, and the strings were so high at the nut, you can't even press down to the first fret. So the dudes at the store cut the nut for free and I got it for Christmas and blah blah blah long story short, the nut wasn't cut so they cut it at the store.

Ever since I've had the guitar, the A string likes to give major fret buzz at the 2nd fret, and a small bit on the other frets around it, but mostly just on the 2nd fret. Now my action is like really high and its a pain in the ass its so high, and I still get a buzz. Should I change my nut? My mum already ordered me one off a website and I'm getting it for my birthday on Monday. Do you guys think was dumb or am I correct?
#2
I think so. Basically you want your strings to be the same distance from the fingerboard all the way down it. An equal action. While you can adjust the saddle anytime, you can only cut the nut once. Well you can make it lower but not higher. So first adjust the saddle until its good, then cut the nut until its good, and you should be fine. If you still have buzz I can't help you, I dunno what it might be.
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#3
Basically you want your strings to be the same distance from the fingerboard all the way down it. An equal action.

Whilst I'm probably not going to be a lot of help here, I'm pretty sure the above statement is wrong.

Just doesn't make sense.

There should always be a little neck relief and therefore it would be impossible for the action to be uniform at every fret.

Hmm, think about pressing down on the first fret. It'd be lovely if the 20 fret were the same distance from the fretboard but I doubt it ever would be.