4G is only used on AT&T models to designate when they are in an HSPA+ area--Verizon models will show 3G when outside of LTE coverage.
Correct.
It'll say "Verizon LTE" or "AT&T LTE" when you're on LTE service. It'll say "AT&T 4G" for HSPA (AT&T's 3.5G service), and either "Verizon 3G" or "AT&T 3G" for normal 3G coverage areas.
It'll ONLY say "LTE" if you've signed up for a prepaid or postpaid plan. If you don't have paid service, it will not say "LTE" -- even if you're in an LTE area.