The 7 card says it can be used in the normal fashion to move a pawn forward seven spaces. It has the special ability, though, to be split among two pawns: moving two pawns a total of seven spaces (e.g., one pawn 2 and the other pawn 5 spaces).
The Amplified explanation you quote is merely telling you that you must use the whole value of the seven and that the pawns so moved might land (that is "are permitted to land") on home or other pawns or slides. They belabor (and perhaps obfuscate) the point by providing a list of several specific examples.
a split may be used to move 2 men into Home
Means that. for moving pawns to home, given that a pawn can only move home by exact count, you can use the 7 card to move two pawns home if the pawns were 1 and 6, 2 and 5, or 3 and 4 spaces from home.
The rest is similar: just more ways in which you might move two pawns. The crux is that the whole seven must be used, and that the pawns being moved are not restricted to "base movement" only, but can move home, land on slides, land on opposing pawns, and so on.