There's a wonderfully specific subspeciality in Roman archaeology that examines the ruts left by cart wheels and even pedestrians; that gives us some of our best information about Roman traffic. The first article I'm aware of to dig into this subject was Tsujimura's "Ruts in Rome" [1990], the ensuing three decades have seen a great deal of interest in the subject, with key articles like Traffic Policy and Circulation in Roman Cities [2011] and The Roman Street [2017]. The noted scholar in the study of Roman traffic, particularly from archaeological evidence from Pompeii is U Mass Amherst's Eric Poehler, author of many papers and and "the one book to read if you only read one on this subject" -- The Traffic Systems of Pompeii [2017]

Careful analysis of wear patterns allows for scholars to deduce the existence of one way streets,

[T]races of wear on stepping-stones, curb stones and corners indicate that the driving direction along Vicolo di Mercurio had been changed from eastbound to westbound (according to Poehler) — this street was a one-way street. More evidence that the street was planned for eastbound traffic is the street profile: every section of the street between two intersections has been widened slightly to the east; the widest part of the street section is the point just before the intersection, where the view was the best.

Yes, there were shops along the way. The Roman "street" was much more than a transportation thoroughfare in town: it was a busy place, and business and social life was conducted all along. Roman streets in Pompeii are abundantly supplied with benches, this was an environment anticipating that people would be "on the street" -- and would stay there, waiting for friends, waiting for customers, waiting for vendors. The poet Martial records the conflict between commercial and practical uses of space, and the intervention of authorities to sort it out:

The rash shopkeepers had taken over the whole city; no threshold stayed within its own threshold. You, Germanicus, ordered the narrow streets to expand and what had recently been an alleyway was made a road. No wine jugs are chained up to encircle columns, and the praetor does not have to walk straight through the mud anymore. The random razor is not whipped about in a thick crowd, nor does the grimy cook shop monopolize the whole street. The barber, the barman, the cook, and the butcher all respect their own thresholds. Now it is Rome, just recently it was one big shop.

Pompeii has on the order of a hundred thermopolia, little fast food restaurants not too different in their narrow shape from old time New York pizzerias. Other sensual delights were found along the street, notably brothels-- and there are graphic signs ("phallus reliefs") pointing the way, found carved into to the streets of several Roman towns, a signal to visiting sailors who perhaps didn't read Latin on just which way to go to find a little companionship, see:Ochlos Nautikos: Leisure Culture and Underclass Discontent in the Roman Maritime World

Roman law notes the responsibility of the aediles to keep streets clear for movement. The jurist Ulpian noted that the street was

the property of the civitas and not of each individual[and ]we have as much right to enjoy them as anyone of the people has to prevent their misuse.

There's also good evidence that streets were blocked as a matter of policy, or that obstacles were removed as a matter of policy, that is, that traffic planning was going on, and a regarded as a responsibility of civil authorities. Householders were responsible for the upkeep of the street in front of their homes, and if their maintenance was found wanting, the aediles could contract for repairs at the householder's expense.

Traffic congestion and conflicts. There's are quite a few references to retinues of important people "clearing the way" for the great man or lady in their litter, suggesting a crowded street. The satirist Juvenal has quite a bit to say about this, and specifically mentions "a mob of litters" as though it's a familiar thing.

You ask a good question about mass events. There were separate entrances for the cheap seats and the monied or noble crowd. The Colosseum of Rome had some 76 entrance gates for use by ordinary folk, and four separate entrances for the Emperor, Senators, patricians and the like. See:Spectators and Spectator Comfort in Roman Entertainment Buildings: A Study in Functional Design; the author finds evidence for a crowd control system in the approaches to the Colosseum.

While we don't have specific information about how traffic control was handled around big public events there are enough references in other contexts to guards forming a corridor for notables to pass through that its reasonable to assume something similar happened here. The Romans were very status conscious, and I don't think Roman senators were pushing their way through crowds of plebs.

You might also speculate that the aediles established one way streets and barricades to move traffic smoothly into and out of such places- we know they used these traffic policies in other contexts, and while we don’t have evidence for it on a temporary basis for event crowd control (because temporary measures leave fewer physical traces, and because we don’t have good street preservation outside the Colosseum) it would be a reasonable guess that the Romans had figured out some organized method for getting crowds into and out of big events. Given the importance of military service to Roman leaders, and the importance of formations to their military, they’d have had routine experience with moving groups of people in an organized way.