Explain both of these points.
Well, here's a map of how it shakes out. The situation in the west is just terrible. There's no good reason I can think of for the federal government to own any land in any fully incorporated state, and if there's a compelling reason for decisions about land in Nevada to be made in an imperial city some 2000 miles away instead of in Carson City, I'd like to hear it. Ownership of any public land should have been transferred to the state government the moment they became a state.
I can think of several reasons why the federal government can and should own land in a state; leaving aside how the feds need some land to operate things like military bases, courts, and administration buildings, there's the fact that the states collectively and knowingly ceded ownership rights over certain land to the federal government when they, the states, created the Constitution (see the Property Clause).
Every bit of land outside the first thirteen legally began with federal ownership: The original thirteen states surrendered all their claims to the land west of the Appalachians when the Constitution was ratified, the Louisiana Territory was purchased by the federal government with federal funds, the Southwest was given to the federal government as part of the treaty that ended the Mexican-American War, and the Oregon Territory was ceded to the federal government by the Treaty of 1818, Alaska was bought by the feds from the Russians, and Florida was given to the feds by treaty with the Spanish. I won't profess to know how federal land in the original thirteen states was acquired (I assume largely by purchase), but the legal right and history of federal ownership of state lands is pretty cut and dry (Hawaii admittedly being something of an odd duck), and has existed since the days of the Founding Fathers. If anything, thirty-seven of the states were wholly owned by the federal government before the feds ceded some of that land to the locals.*
You're free to argue the policy wisdom of retaining federal ownership of land vs. ceding all of it to the states, of course, but legally the issue has been settled for quite some time now. Don't forget that the federal government is entirely a contractually-created creature of the states; if they felt that the feds should give up all of its land, they could have made it that way. For that matter, they still can. Instead, they consciously surrendered some of their own land (not a small concession, if you know how rancorous those fights were in the colonial days), and have not made any real concerted effort to change the situation since then.
In the meantime, regarding Nevada specifically, the reason it's federal ownership rate is so high is simply because no one wanted to buy land there when it was first offered: I don't know if you've ever been, but there's a reason 95% or so of the population lives in only two counties, and if hadn't been for a silver boom (and later legalized gambling) I'd wager Nevada would never have reached the population rate it takes to become a state: the place is largely uninhabitable.
*We are ignoring the whole issue of people who lived on said lands before the territories were ceded to the feds, most notably the Native Americans but also French, Mexican, British, Russian, and even American settlers, only some of whom were covered by the treaties encompassing their territory and only some of whom previously answered to the sovereign who handed the land to the federal government.
Well that, and when Georgia and Virginia had to give up land to the Federal government it was ruled that the federal government can only hold land in trust for the formation of new states and not for any other reason, and must give that land to the state when formed.
Source? The closest I've heard of this is Pollard's Lessee, which only a minority of scholars have read it that broadly, with the general consensus, including the Supreme Court's, being that the ruling was far more narrow than that.