Overhead is to reduce the size of armies. A lot slower recruiting squads when your overhead hits +100%
As for the costs, it's the same for all. You could recruit 100 inft, 50 vech or 33 mechs before your overhead hit's +12%. So you can recruit more inft, however because vechs and mechs have higher damage it all works out to be the same.
As for the second question; it doesn't matter whether your units are split up in single squads or packed in to one squad while in battle. The outcome will still be the same. It would be a heavy waste of oil though, however it's good for bluffing and advisable for spams