I have a few questions all rolled into one, so I'm going to bullet them for ease of reading:
Consuls had very little real power in the principate, although they did fulfill certain ceremonial and religious functions. During the empire, most consuls did not actually serve for very long: the ordinary consuls, who still technically gave their names to the year (although dating by emperors tribunician powers quickly became the most common form of year dating), took office and then usually stepped down after 2-6 months. This allowed for new suffect consuls to be elected; these in turn might only serve a few months. It was therefore not uncommon in any given year for more than six men to be consul, thus spreading the honor around. Obviously, being an ordinary consul was more prestigious than being a suffect, although often an ordinary consul had previously served as suffect.
The consulship in the empire was therefore less a practical office than an honor and a status. But while consuls were basically ceremonial, consular men were very important people in the empire and its administration, and were eligible for the most important provincial governorships, either as legati Augusti (the emperor's lieutenants commanding provinces with military forces) in key provinces or the few proconsular governorships, with the proconsular positions in either Africa or Asia generally seen as the pinnacle of a senatorial career.
So Imperial consuls in their *very* short term in office didn't do much. But generally they had done quite a bit to warrant the honor, which marked them out for even more important assignments afterwards.