Basically, what is the correct terminology when referring to the people before and after Rome? When did they start and stop being Romans and how do you refer to them? When did those people become Italians?
Well, the correct term is "italians". The italian peninsula was inhabited by different tribes that were eventually assimilated or destroyed by Rome. These people were always italians, what changed is the political entity. So if you are speaking of the population as a whole you can refer to them as "italians". Specifically, the people that emerged as Romans were the Latins.