Yes you can camp for free in national forests.
Free camping in national forests is allowed unless there is signage that says otherwise in certain areas.
In a national forest you can do dispersed camping in either tents, your vehicle or motorhome or Travel Trailer as long as it can fit.
My husband and myself and kids go camping in our travel trailer in some national forests each year and it's so relaxing.
We have a generator and solar panels that we use for electricity while camping.
Just find a place to camp and you should not be bothered.
National forests are okay to camp on but just note that some public land does not allow camping just because it's public.
Just lookout for signs and you'll be okay.
On some public land you can legally camp for 4 days to 7 days and in some cases you can camp on the public land for up to 14 days.
However after the time limit you must move off the land for at least a few days to a week and then you can return.
So technically the land if it's public camping land that allows camping you could live on the public land for life as long as you move out every week or so for awhile and then return.
But just be aware that just because the land is public land does not mean that you can camp or sleep on it.
Some public lands are just for day use and not for overnight camping.
If the public land allows camping it will usually say it does allow camping.
If the public land does not allow camping then once again there should be a sign saying so.
But if there's no sign and you're not allowed to camp overnight then if you do the worst that would happen is a cop comes knocking on your door, vehicle, etc and tells you that you have to leave.
If you come back and camp after being told not too then you can get a ticket.