I know that there were two different forms of it.
The first one is senators sitting parallel to each other like the seats of a football stadium and there was this corridor between them, so it was like the British House of Commons.
The other form was just like an amphitheatre, with the senators sitting through a half circle.
Does anybody know which form was present during which eras? The only hint I have is that Caesar was murdered in the Theatre of Pompey which had the amphitheatre formation, but many media sources depict the first corridor formation so I need your help in determining during which time in its history it had the corridor formation and in which time the half circle one
The problem you're having is that you imagine that there was a single place the senate met. This is erroneous. While modern legislative bodies meet in a established place (the senate, of course, was not a legislative body and could not promulgate legislation), otherwise public business cannot be formally conducted, Roman political bodies could meet pretty much anywhere that met whatever the requirements were for that sort of meeting. So the electoral comitia might take place at the Capitoline, in the forum, or in the Campus Martius. The senate had no legal rules of convocation, but traditionally a curule magistrate sent out a summon to the senators that a meeting would occur at a particular date and place. The only requirement for a meeting space was that the area be dedicated as a templum (not literally a "temple" in our modern sense, but a space marked out for augury). From there a consul would take the auspices, etc. but the point is that the summoning magistrate could call senatorial meetings anywhere that the senate could all fit and that met the requirement as a templum. The senate did have an "official" place of meeting--the curia in the forum--but other curiae existed, most notably the curia Pompei in Pompey's theater, which was outside the pomerium and was intended to serve as a meeting place should the presence of promagistrates be required. And any augural space could be used--in particular the senate met often at several temples on the Campus Martius, and Cicero convened the senate during the Catilinarian Conspiracy not in the curia but in the Temple of Concord, literally across the street, for symbolic reasons. The precise arrangement of these particular areas was different, although there's zero evidence to suggest the seating of the senators mattered at all. The curia in the forum had some kind of benches arranged in parallel, with two groups facing each other and a space for speakers in the center. Pompey's curia may have been in the exedra of the theater, which would have placed it in a semicircular area--however, we don't know that, we only know that it was somewhere in the portico, which suggests to me that instead the entire portico was dedicated as a templum and the whole portico space used. If true, then meetings in Pompey's theater (used as one of the main meeting places outside the pomerium and especially often between the destruction of the curia in 52 and its rebuilding in 29) would not have looked especially different from those in the curia.