Some thoughts that have been on my mind:
Although these categories are just to try to understand what is going on, because I don't think it is possible to have precise boundaries here, it seems, in a very very broad way, that the protests were comprised of (i) peaceful demonstrators, part of which were following the Free Pass Movement and even those that don't usually had some kind of identifiable argument to their protest; (ii) vandals, some of which are violent against the police but in general destroy public and also private property and most of the time have their faces covered (some demonstrators also have they face covered, but it seems more prevalent among vandals and criminals); (iii) criminals, what distinguishes them is that they not only break stuff but also break in and steal from stores, they appeared on the scene of many demonstrations late at knight.
Peaceful demonstrators were many times seen confronting vandals to stop them in their acts of violence or property damage. When significant number of vandals gather and take the front the peaceful demonstrators start to leave the scene. Most peaceful demonstrator don't burn anything, but some burn tires to stop traffic, while vandals burn anything, including vehicles. Vandals burned mainstream media vehicles and also tried to stop some reporters from recording the images.
Somewhere among vandals and criminals there is a group that is particularly offensive against the police and do whatever they can to resist and keep pushing forward even under heavy fire of tear gas and rubber bullets. Please note once again that I'm trying to categorize to facilitate the discussion, as I'm certain there were many variables in each incident.
One thing that is very clear is the police violence, not only against vandals and criminals but also against peaceful demonstrators and actually anyone that is around when they decide it is time to start shooting. There was a number of cases of people that had NO involvement with the demonstrations and were just going home or were just there in the street for any other reason that suffered injury from police violence, mainly with the use of pepper spray, tear gas and rubber bullets. Since police violence is ordinary business in Brazil, I think this gained notoriety because of the many reporters that were seriously hurt and also because police violence is much more common in poor neighborhoods, while now it is also affecting the upper middle class. Elderly people, pregnant women and children have been hurt, as mentioned by Iron.
The involvement of BOPE, as also mentioned by Iron, is worrying. Has anyone seen the movie "Elite Squad"? It shows BOPE officials torturing drug dealers (or supposed drug dealers) in Rio de Janeiro's slums, besides a lot of other violent behaviour. Maybe a tactic to condition the population, to make us think this is normal?
Regarding the Government, although I'm sure there is much more to it, the local state and city governments did seem surprised by the demonstrations. I think of this because in the beginning they were very rigid in saying that there was not going to be any negotiations and that the bus and other public transport fares would not be reduced. However, a few days later when the demonstrations became huge, they backed down but did not seem happy with this outcome.
In the case of the Federal Government, the only thing that seems clear is that they quickly embraced the demonstrations as democratic when they grew in size but warned against violence and damage to property. I'm worried because Brazil recently "revamped" its arsenal and security for the World Cup games next year, including a few drones. We could already see in the games of the Confederations Cup that the police was instructed to use all means to keep the demonstrations at a distance of at least 3 kilometers from the stadiums while there is a game going on. The police took this seriously and the result was a lot of violence and injured people around the stadiums. Some drones were bought to be used specifically during the games.
Also, it seems that ex-president Luis Inácio Lula da Silva and the Labor Party marketeer had a heavy hand in the Government's decision of embracing the protests as democratic. The media reported that Lula also influenced the decision of São Paulo mayor Fernando Haddad to back down on the bus fare rise.
Given that Thursday, June 20, there were 1,2 million people protesting in 388 cities, it seems that a significant part of the people of Brazil are backing up the demonstrations. However, it seems that many disapprove, on many grounds: because they don't think it is fair to stop the traffic, because of the resulting violence, because they think the demonstrations are inefficient or, more importantly, because they think the demonstrations are attached to a left wing revolutionary ideology or because they think the demonstrations are attached to a right wing fascist ideology (this latter being covered on the link posted by SMM).
Regarding this left wing x right wing problem, I find it very interesting that each side is pointing their fingers to the other. I don't know what is the truth in this debate but the rhetoric of both right and left wing is pointing towards a totalitarian regime (or, more correctly, overtly totalitarian regime).
I think it is important that the mainstream media which originally was kind of divided but in most part against the protests were quick to embrace the protests as democratic, following or actually anticipating the Government's position. The mainstream media has repeated constantly that the protests are not of a political nature, which makes me wonder...
Well, I have almost no answers and many questions. We know it was not spontaneous because there was an organization behind the beginning of the protests, but why the sudden increase in numbers, why now? Has it been planned for a long time? Who is going to benefit from the protests?
Trying to think in a very broad manner about the general situation of the world - a one world government of psychopaths and authoritarians follower - and the very rapid "rise" of Brazil as an important player in the world stage, probably meaning being a more active chess piece in the hands of the Controllers, my guess is that things are going to get worse. In general my thought is that we are moving towards a more controlling State, with fewer liberties and more violence for those who try to oppose it. They have guns and we have none (gun control is very strict in Brazil). Now they have drones. And now they have an uproar in the streets, which is already giving cause to violence. But until now we saw very little real bullets, but maybe they will soon be the norm against protesters?
Can it go in the other direction and all the requests of the protesters be fulfilled? No corruption, good education and health care for everyone? It does not seem likely unless the whole Brazilian Government (and all its branches) are rebuilt from the ground up, not to say having to diffuse the knowledge of psychopathy among the people so they can no longer re-infiltrate and take charge again.
All in all, maybe it is one more sign that the Cosmos is going to "clean house" and it is "knocking at the doors"?