• Does the LNT ethic try to protect wilderness preserves only, or the environment everywhere?
  This is the displaced impact issue. In my opinion, the goal is to protect wilderness preserves only. While protecting the environment everywhere is a good goal, it will take much more effort, so it should be considered a separate issue.

  On the other hand, see the "dualism" section below.

• What is being protected here?
  What's the goal? To have pristine wilderness? To minimize the impact on wildlife? To make sure that the land, even if impacted, remains ecologically self-sustaining? To have land that looks to humans as if it's untouched?

  This Backstory episode points out that most land in America has been affected by humans for many hundreds of years. (slash-and-burn was used before the Neolithic)

  The Wilderness Act of 1963 defines wilderness as land "with the imprint of man’s work substantially unnoticeable". So the goal is more to appear to humans to be minimally used. (of course, we know that federal preserves serve dual purposes: human recreation and biological conservation, so appearance isn't the only issue)

• Does the LNT apply in rarely-used national forests? What about private land?
  These two comments along with this one answer that nicely, I think. "The rigorousness with which LNT has to be followed is directly proportional to the number of people using a wilderness area."

There are some other philosophical issues:

• If humans and nature are defined as entirely separate (AKA "dualism"), then some problems pop up. Perhaps some very serious problems.
  "some arguing that there is not really such a thing as nature at all beyond some self-contradictory and even politically dubious constructions of an ideal other that ignore the real human-environmental interactions that shape our world and lives.[7] This has been alternately dubbed the postmodern, constructivist, and most recently post-naturalistic turn in environmental philosophy."

More things to read:

• Glossary of Terms in Environmental Philosophy — see "wilderness", "nature", etc
• Stanford Encyclopedia of Philosophy