>What the hell is the trussrod?
A truss rod is inside your guitar neck similar to a spine. You should be able to access it from a little plastic plate in your headstock (remove the screws) or under your scratch plate if you have a fender strat (certain models). You will need an Allen key to tighten or loosen it. If your guitar neck is bowed either way you can straighten it - Do not use the truss rod adjust the action (this is done by adjusting the bridge and/or nut) however action is sometimes lowered as a result.
Always use the right size Allen key so you dont strip the rod and only tighten an eighth of a turn at a time, you don't want to strip the internal thread. If you have to replace a truss rod on a cheap guitar you may as well buy another guitar.
>The action is really low at the first fret, and probably three times higher at the 24th,
Sounds normal to me.
As I said before hold down the string at the first fret with your left hand and with your right hand hold down the string at the 12th or 14th fret at the same time. Look along your neck and check the straightness against the string.
>first the .52 gauge string tears the nut,
Sounds like you have a plastic nut. Locking nuts keep guitars with tremolos in tune a bit better.
If you have a plastic nut get yourself a 6B lead pencil and shave (with a razor or sharp knife) some of the graphite into the nut behind the strings. Lead pencils by the way are made of a graphite and clay mix not lead.
The graphite acts as a lubricant. Yngwie model guitars have a brass nut and you lubricate them with oil. As you use the tremelo the string slides up and down in the nut and acts like a file and eats away your nut.
If your string gets caught (due to friction - wedging) in your nut it doesn't return to the original position and hence gets out of tune.
Cheap tremelos can also cause a guitar to go out of tune if the spring action doesn't return the string to original position.
>then the store chips the headstock, then I chip the headstock, then my friend scratches the body, then he chips the body..
I remember reading that when Vito Bratta gets a new guitar the first thing he does is put a chip in it then he doesn't have to worry about handling the guitar with kid gloves till it gets a chip.