A "surface border" is a loop of edges that create a hole from the exterior to the interior of the object. A SketchUp solid must be an air-tight surface enclosing a volume. It can't be air-tight with a hole! Such holes also create a place where the model has an infinitely thin surface exposed, which is a mathematical abstraction that can't exist in reality. The reason Solid Inspector doesn't fix these is that it can't guess your intent. The fix requires somehow closing up the hole, but there are almost always multiple ways to do so. So, click the surface borders part of the SI window to see what it highlights and then draw additional geometry as needed to close the hole.
"Internal face edges" means pretty much what it says. There are faces with edges protruding into the interior of the object. SI can often fix these, so try clicking the "fix all" button and see what happens.
