#2
Yes.

Apparently, because that's what happens on all the guitars I've owned.

Then again. Maybe it's not. Preferance maybe?

2004 MIM Strat w/ Fender Hot Noiseless pickups
Sovtek MiG 60
Avatar 2x12 w/ Celestion Greenbacks
Snark Tuner
MXR Custom Comp
Fulltone Full-Drive 2
Dunlop JHM3 Univibe
TC electronic Nova Delay
TC electronic Arena Reverb
#3
It is. It's called neck relief.

Your neck is slightly bowed, so that no matter where you fret, the string won't touch the other frets. You can check your neck relief by fretting the first and last frets on any string and checking whether it touches any other frets. It shouldn't.

If it does, you should have your action or truss rod adjusted.