My action seems to get higher as you go down the neck, as in higher towards the bridge?

is this normal?
It's normal, as long as the increase isn't anything major. If you still have the setup book for the guitar, it should say about string height at 5th and 12th probably.
Think about it - if the action was even over the length of the string it would make contact with the frets above your finger.

Fret your low E at the first and last frets and see if you can slide a credit card between the 8th fret (the actual metal part) and the string. If there's a reasonable gap your truss rod needs a little adjusting.
American Deluxe maple board Strat
Hot Rod Deluxe
Fulltone Fulldrive II mosfet