What kind of suffrage did they have? How where elections run? Could anyone run for office? What kind of offices where there to run for? Also, how did these republics react to the formation of the U.S.A. and it's constitution??
I would also be interested in hearing about the republics in older time periods, ancient Athens or similar states would also be interesting. Also, if there where republics outside of Europe, how did they function??
First of all, as the wording of your question suggests, the communes of Italy, like the united states, were not democracies, they were republics.
To make a blanket statement about all of the states of northern Italy across the 500 year stretch of the high and late Middle Ages would be a bit tough. Generally, the vote was closed, and certainly limited to male citizens, oftentimes voting in blocks similar to the electoral college. This setup often allowed for narrow oligarchies to control the governments. This is, however, a blanket statement. Popular revolutions occurred throughout the period, particularly from the second half of the 13th century through the fourteenth, and by the fifteenth century, many cities were ruled by strongmen. Oftentimes seats in offices were reserved for members of guilds. Sorry if this is vague, the governmental structure cities of northern Italy varied widely and was constantly changing throughout the Middle Ages.