#1
Just wondering, would raising your action make the strings sharp, or flat? and string gauge, are thicker strings sharp or flat?
#2
Properly set up, nothing would do anything to your intonation.

Otherwise, raising action would probably make the upper frets sharp. Not sure if string gauge would affect your intonation, but if your action is low enough, it may give you some buzz.
Ibanez RGA121 | ESP LTD H-1000
Axe-FX Standard
#3
Anything you do to a guitar that affects the overall length of the string from the saddle to the nut will throw out your intonation it may be so slight that you won't notice but raising the action increases the string length and lowering the action will decrease the string length. Same for Truss Rod adjustments because you are either straightenig or bowing the neck.
YA GOTTA HIT IT ON THE ONE
pics of gear updated on profile 11/16/09
#4
String gauge will affect intonation, whether or not the G string is wound or not will affect intonation, the current temperature will affect intonation, how new the strings are will affect intonation, how hard you press the strings will affect intonation, the list goes on and on.

When you set the guitar up, you're generally adjusting to work well with a specified set of strings and with a specified amount of action. The rod and the intonation are adjusted accordingly and most other factors won't affect the intonation enough to really be noticed.
ESP LTD EC-256 and a Fender Deluxe VM