The Roman system of Republic included a Plebeian Council and a Tribune of the Plebs that, in theory, allowed common citizen interests to be represented by the patricians and in the Senate.
My question is about whether this representation extended to Rome's war efforts, diplomatic relationships and geostrategy. How deeply were citizens able to embed themselves into Rome's most important and ambitious drivers of wealth and fortune?
On a similar note, was it commonly believed among the commoners during Roman times that Rome was an empire like Alexander's and others before it?
Answering these questions would require roving over more than 400 years of constant tumult and innumerable shifts in governing coalitions, ideals and political thought.
The Roman system of Republic included a Plebeian Council and a Tribune of the Plebs that, in theory, allowed common citizen interests to be represented by the patricians and in the Senate.
This is an interesting issue, and clarifying the questions around it would go a long way towards providing the answers you're looking for. Relating it to the other questions you ask would cause the complexity of any reasonable response to spiral out of control, however.
I'd suggest isolating this issue in a separate thread -- the narrower (but still very comlpex) title issue would help to attract the interest of relevant experts and once answered the other issues would be simpler to deal with.
I'll give you a cursory response which is as good as can be managed to these sweeping issues: The Roman Empire was an absolutism where distinctions between patricians and plebs no longer mattered so much any more. What counted were the opinions of the soldiers generally and the Praetorians in particular.
The remaining vestiges of constitutional rule were only window dressing. Emperors did tend towards populism to be sure, but only in the narrowest sense of pandering to the mob in the city of Rome itself. The poor elsewhere counted for little politically, and the slaves for nothing at all.
Sorry for putting this in dot points but there are a lot of things to note:
The notion of a 'plebeian' as opposed to a 'patrician' was of relatively little import in the Late Republic or Empire, especially when it comes to legal rights and political status. Whether or not someone was a plebeian did not really determine their political status.
If I'm reading your question correctly, you confound 'republic' and 'empire'. It would help if you clarified which you are referring to.
In answer to your question: Rome's war efforts and foreign policy were usually the exclusive preserve of the Senate. This convention was most famously disrupted in 133 BC by Tiberius Gracchus who, upon the death of Attalus III of Pergamum, appropriated the fortune he bequeathed to Rome in repudiation of the Senate's traditional jurisdiction in foreign affairs.
Romans used the language of empire and understood themselves as such. I know that Trajan in particular was fascinated with Alexander the Great. Perhaps others have more information on this.