Considering that Space X have just announced that their BFR can take anyone anywhere in the world in under 1 hour, that would be enormous speed, does this rocket not produce sonic boom? If not is it because of its shape and that it does not have wings? Will it ever be allowed to fly across the US above the oceans and anywhere at those speeds considering again sonic boom?
The only way to get anything that far that quickly is to send it into space, and that's exactly what Musk is suggesting. The BFR will launch a passenger carrying spacecraft out of the atmosphere and into a sub-orbital path, it will re-enter the atmosphere close to its destination. Rockets launch pretty much straight up and a sonic boom would have to compete with the rocket itself on noise. Once above the atmosphere there is no sonic boom because there is no air.
On re-entry all spacecraft create a sonic boom, for most of the re-entry this is inaudible from the ground because the air is extremely thin, once in the lower atmosphere it gets louder. By the time the spacecraft gets low enough to create a really big sonic boom it's usually at a subsonic speed and would not make any boom at all. The shuttle and Apollo spacecraft both created sonic booms on re-entry, that's covered in this Space SE Question.
So, are sonic booms a problem in this idea? It depends, the space shuttle re-entered over the continental US many times and it never bothered anyone, but if it was happening a few times a day it might be a problem. You could get around that for the most part by re-entering over sparsely populated areas or the ocean.
More likely it's not the sonic booms that people won't want from a noise perspective, but the launches.
Since the rocket will be traveling through space, there will be no noise on the ground during cruise.
As pointed by @DeltaLima in the comments, a lot of satellites are crossing the sky above us at this very moment. Since there is no air in space, no sound can be heard, especially from that distance.
The only noisy parts will be the takeoff and landing, but with carefully selected location, this shouldn't be a problem.
I doubt it. Sonic boom/s may well occur but likely (or could be specifically planned by routing etc) to occur in upper atmosphere/away from population centers.
The rocket seems planned to take off from an island or floating structure (judging by the graphics, which showed a ferry to the launch site), which could easily be tens of miles away from land if that were an issue. That distance might be enough to mitigate a lot of the launch noise.
As for landing, it's probably possible to come into landing along such a trajectory as to not be near a city when excessive noise will be produced, either by coming in over the ocean (in the graphic's example) or even by 's'turning around populated areas, shedding speed in the same trajectory (the space shuttle bled off speed this way, I believe).
Note that military craft produce booms frequently (although AFAIK they try to limit proximity to populated areas), as does any orbital (and most suborbital, although not so many of those fly these days) rocket, and Concorde produced booms. So:
Will it ever be allowed to fly across the US above the oceans and anywhere at those speeds
I don't see potential booms impacting whether it is allowed at all. Where it is permitted to be routed/produce booms, and how frequently, are open questions.