1) No, Praetors could also lead armies. The Conculs were given the most important assignments, though. And yes, the late Roman republic did have some trouble keeping order in the more distant provinces, but this was often for political rather than military reasons. At this point her external enemies were mostly too weak to contemplate attacking Rome.
2) No, the cities of Italy were "allies" and had their own government. This government was expected to obey Rome, though.
3) See
this thread.
4) Check out the recruitment viewer. It should be somewhere inside the folder where you installed EB (IIRC the install file is RV.exe).
5) Yes: they will educate your governors and generals (in game: give them ancillaries and traits).
6) The military buildings of other cultures are often useless. You can tear them down.