As much as I enjoy the series, it does take a number of liberties (as you might expect). For instance, at first Pompey is described as consul of Rome. The problem is, that part of the series takes place in 48 and 49, while Pompey hadn't been consul since 52.

While the show does talk about the Senate House, and if I remember right, it is set in the Forum, (Curia, properly named), that Senate House actually burned in the riots following Clodius' death in 52. The Curia Julia also wasn't finished until after Caesar's assassination.

Where the Senate met in the meanwhile was in various temples around the city, even before the Curia burned down. Because, after 52, Pompey was proconsul of the two Spanish provinces, when he attended Senate meetings, they had to be held outside the pomerium, the sacred boundary of the city past which military commanders, with a few exceptions, couldn't come without dissolving their command. For those meetings, they used the Theater of Pompey. This was an actual theater; in fact the first permanent theater in Rome. It still exists and has been excavated. The Wikipedia page has several plans of the theater, including one from the 3rd C CE. Because it's an actual Roman theater, seating is semi-circular, and faces a semi-circular... it would be called "orchestra" in a Greek theater; I'm not sure what the Roman term would be, before the facade.

I don't know if we have evidence for how the space was used in a senate meeting. It seems reasonable to suppose that speakers would use the acoustics that the theater was constructed for, that is the orchestra and the facade.

Incidentally, this theater is the place the Senate met on the Ides of March in 44, and where Caesar was assassinated. The fact that this was Pompey's theater allowed Plutarch to tell that ironic anecdote of Caesar dying at the feet of Pompey's statue.