In answer to your question about files, most guitar shops would not carry them as they are sales people and not repairers, some will be of course, try stewmac.com and while you are there look at their graphlon nut, I have one in a Strat and it is really good, the trick to filing is to know how deep you want to make the groove and put a spacer between the fret board and the string space so when the file bottoms on the spacer you have reached the desired depth, it's standard to use feeler gauges for this, you also use them before you start to see what the current depth is.
The nut should just tap out but check the finish to see if it is sprayed on the existing nut. If it is you will have to mark it with a sharp knife so it does not chip when removing the old one.
When you file the nut for fit, lay the file on a bench and slowly rub the side of the nut over the file, this is how you fit a key in a shaft and gear, you keep the flat surface in contact with the file and don't get rounded ends and gouges. Only take a couple of 'thou off at a time, use a micrometer if you have one or a vernier, you want an interference fit, just tap in nicely.
Good luck
Clive