Is there a fee for grazing on Federal land?
Yes and has been in place for many years. It is one of the ways that the federal government allows use of the land for the public good. The money collected goes to offset the cost of maintaining the land (such as wild fire suppression costs).
Yes.
The fee doesn’t actually cover the full cost of land management, but it isn’t clear that it is supposed to. Right now, it is $1.35 per head per month, which is the minimum it can be, due to a 1986 executive order (would have been President Reagan).
http://www.denverpost.com/news/ci_22704766/federal-grazing-fee-stays-same-rekindles-debate