Is this unique to the USA, or now common elsewhere?
No. It is common throughout the developed world.
How long has this been done, as opposed to keeping all the inmates constantly locked in their own cells and only seeing each other when eating in a dedicated eating place or when brought outdoors once a day for an hour or so?
Before the late 18th century, imprisonment was not a punishment - it was a place where you were held while awaiting trial or punishment: execution, corporal punishment, humiliation or transportation. However, it was not uncommon for prisoners who had been acquitted to still be held because they couldn't pay the cost of their pre-trial imprisonment. The 1779 Penitentiary Act introduced solitary confinement, religious instruction, and a labour regime. These types of prisons were not actually built until the 19th century and saw increasing use as the death penalty became applicable to fewer and fewer crimes. These types of prisons spread across the western world and it is this 100+-year-old image that you are thinking of.
However, for some reason, solitary confinement and individual prayer seemed to cause no improvement in the moral state of prisoners. Therefore, since the early 20th (yes, 20th) century most prisons had communal mess halls and recreation yards for use on the weekend. In most, prisoners worked during the week, around the prison or outside in things like quarries and road construction.
Starting in the late 20th century "hard labour" was largely done away with and prisoners were offered work or education opportunities. They were confined to their cells at night in medium-security and higher-level prisons but low-security prisons often work on an honour system and cells are not locked. Developments such as day-release and weekend detention have influenced prisons. Many northern European countries have literally open prisons where you are free to come and go so long as you spend the nights there.
Only the worst of the worst are kept in super-max prisons and only the worst of them are kept to their cells and isolated from the rest of the prison population. Those are the people who get 1 hours recreation only. That said, prisoners have rights and their physical and psychological well-being are the responsibility of the State. Doctors and psychologists examine prisoners and balance risks to society against the rights of the prisoner.
I've worked inside super-max prisons as a contractor and they are bleak and scary places but most inmates are free to roam around the grounds and other common spaces. I've also worked in low-security prisons and they are very different - still not nice places but spartanly comfortable.
If you get sent to such a prison, can you choose to get a normal cell if you don't want anything to do with these violent, crazy people? Or are you forced to endure that living nightmare and constantly be on guard?
You're a prisoner. One of your punishments is having your freedom of choice taken away from you. The system will tell you where you sleep, where you eat, where you can go and when you can go there. If you are a "violent, crazy" person then you will be in a super-max prison with other "violent, crazy people". If you are a white-collar criminal, you won't be.