US Army Enlisted Ranks & Length of Service

[Mahatatain]

I'm just working out some NPCs and I just wanted to check that I understand how the enlisted ranks of Private E-1 (PVT), Private E-2 (PV2) and Private First Class (PFC) work in reality in the US Army.

Am I correct in thinking that promotion to PFC is automatic after about 6 months of service?

Assuming that I'm correct then I also assume that almost all Privates will have been promoted to the rank of PFC by the time a T2K campaign set in the year 2000 starts?

Also, purely for my own personal interest, what is the difference between Private E-1 (PVT) and Private E-2 (PV2)? Is a recruit in basic training an E-1 and they become an E-2 after they have passed basic training?

Thanks for any help.

PS - I'm British by the way which is why I'm asking these questions.