#1
Well I hope this is the right place to post this, damn my newbness :p

Not too long ago I bought me a nice little LTD EX 400
Explorer style body..

I love this thing but there is two things that are kind of annoying me.

First off the guitar is very top heavy and if I let go of the neck falls forward xD

Second I noticed the strings are pretty far up above the fretboard. The fretwire is pretty tall and it has an earvana compensated nut that seems to be higher than others.

I used an Ibanez Iceman to compare it to. If someone could help me solve those two problems I would be beyond grateful.
#2
Take the nut off, heat the glue ( hopefully it's glue ) with a hairdryer to soften it and gently take it off and evenly sand it down, reducing action at the head.

Get a strap which grips better, such as a leather strap, adjust the angle of how you hold the guitar and generraly muck about until you find something that works.
#3
Not much i can say about the top-heavy part, my friends SG is the same way. As for the action, lower the bridge, and DONT **** WITH THE NUT. You can really screw a guitar up by doing that, take it to someone if you really honestly, truly believe its the nut. Im pretty sure its just the bridge, screw it down little by little.