No.

Not necessarily needing from the original Simcity series to play Simcity 4, but to play Simcity 4: Rush Hour, that's where you'd need the first Simcity 4.

Yes. The official name is Simcity 4.

SimCity is NOT known as that, nor will it be in the future.

Simcity 4: Roads, Ground Highway, Elevated Highway.

Simcity 4 Deluxe (Simcity 4 and Simcity 4 Rush Hour Expansion Pack): Streets, Avenues (Four-Laned Roads),Simcity 4 Transport, Rail, Elevated Rail, Monorail,Subway, and More Download-ables on Simtropolis.

No, you can't use SimCity 4 mods on SimCity Societies.