Erm...as a senate you won't have the power to order around people like the senate once did to you. Sorry, no sweet revenge and proper manipulation of the patriotism of your fellow country, just like you couldn't manipulate the faithful Catholics as a Papal faction in MTW would do if it was A.I.
Yup. Senate just plays like your run of the mill faction, from what I've seen.

It is also bugged and I never heard of anyone ever winning the game.

There are also reports of random CTD's, though the consistent "senate tap" one is there no matter what.
About these bugs. Could I get some examples? As of now I am going to start fresh on RTW now that I've patched up to 1.5 (by that I mean playing each faction on easy, then replaying them on medium, etc.). Following this order, the Senate would fall as 4th, so I'd like to know of any outstanding bugs besides the "senate tap" one. That is one I think I can remedy by some well-placed modification, and if worst comes to worst I can just try my best to avoid it.