How were there free men in rome who were not citizens ?

They may be plebians(common people), who is different from patricians( nobles, wealthy landowners, or old families). Only Patricians can vote

They made a checks and balance system to equal power within the branches. the "check" meant that one branch would watch one branch and "balance" them if they were too powerful. if you want more info on this, i would just google checks and balance system.