I'm looking to build my first guitar in the near future but something got me thinking about how the action on a guitar should really play. I currently have an ESP/LTD M-200FM and I was adjusting the neck and action and realized the action is substancially lower at the nut than the 24th fret. So I'm wondering, is the action supposed to be at the same hieght across the entire neck? Because if I lower my bridge any more, I get quite loud string noise and some dead notes. Should my nut be higher?

no, its quite normal to be higher at the body end than the nut. Its possible to get the action quite low at the body end but you'll never get it as low as it is at the first fret.