Yeah it works out about that financially
Camp pay will there or ther abouts pay for your flights fees etc
You should budget for your traveling however. More below...
We had a day off a week except for during staff training week
Depends on your camp but generally you can hang around camp (days by the lake etc), head off with your new American friends (they usually have cars), or camp will put on trips (theme parks, city visits etc)
Your J1 visa allows you 30 days travel throughout the USA. Only restriction comes if you wish you travel to Mexico or Canada as you may run into issues with immigration as the visa technically is invalidated when you leave the US. There is plenty of information online about it.
You can book your flights to return any time in that 30 days
My camp was in east Pennsylvania so I stayed for 2 weeks after camp and visited NY and Washington staying in hostels. I’d recommend not making fixed plans but having an idea of what you want to do. You will find lots of people on camp have similar plans and it’s good to travel with new friends