Return homemaths through spreadsheets

Modelling: M1 The Friendly League

The top five teams in the local Friendly Football League are about halfway through their season. To work out their positions in the league they use the current FA scoring system of 3 points for a win, 1 point for a draw and 0 points for a loss.

Thus, DEF C are in the lead by one point.
(a) What would happen if the old scoring system (2 points for a win, 1 for a draw) were used? Do Barking Mad still come bottom?
(b) Who comes out top if an away draw scores 2 points?
(c) Are there any teams that cannot attain first place under any fair scoring system?