It is not normal.

Cheap guitars are notorious for coming from the factory f*cked up.

It sounds like you have a situation common on some cheap electric and acoustic guitars. You need to get your nut adjusted to adjust the action. You might have a truss rod, and it may be used in the adjustment process as well.

You do not know how to do this. I repeat: you do NOT know how to do this. Spend the money to take it to a shop and get it done properly. Then learn yourself for next time, maybe. It's not hard, it's just that you don't know.

http://www.acousticguitar.com/articl...articleid=7643
http://www.fretnotguitarrepair.com/Repairs2.htm

etc.