Citizenship in Rome was tricky. In the beginning, Only men over the age of 15 became citizens. Those citizens got to wear white togas to separate themselves from other non-citizens or slaves.
As time went by citizenship varied a lot. All free people became citizens. A full citizen was able to vote, marry freeborn people, and practice commerce. Other citizens could not vote or run for office but they had basic rights. Another type of citizen could not hold office or marry, but they could vote and practice commerce.
The senate of Rome has been around since the beginning of Rome. It started off as a group of 100, which transitioned into a group of 300 and kept expanding as the senate was the most powerful governing body. This stands until stronger emperors began taking more control and the senate ended up powerless.
After the expulsion of kings from Rome, the Republic was formed. Senate was extremely powerful and instead of making one head of the state, they elective multiple executives that were called consuls.
As tradition, plebeians and patricians were supposed to be separated. A plebeian wasn't even allowed to marry a patrician. The two had different representatives for government. The plebeian representatives were called tribunes and had the power to veto the senate.
The Roman Republic had an important belief of equality under the law. To keep this going, the government leaders carved a bunch of important laws into 12 tablets. The first Roman Laws put into writing. Every citizen was granted equal treatment under the law but lots of the laws were extremely harsh.