The scale of the HQ determines the range of their supply. Isolated units obviously won't be supplied, and if an HQ moves it's position or is hit it can't provide supply for the following turn. This all seems fine, but I return to the length of a scenario and have to ask if, realistically, supply is all that crucial. Unit morale is handled well though, with units that become disrupted suffering attack and defence penalties. Of course there are a whole bunch of other features.
Units can assault to force defenders to retreat, much the same as a melee in the Battleground games.
Artillery fire is preset and occurs during the following turn, so must be preplanned. Air attacks work in the same way, which I found very limiting. This Unit Info box pops up whenever you scroll over a unit. The Fire Cost is the number of AP's required to fire What really hinders the interface and the user-friendliness of East Front is the abysmal documentation, which includes both the help menus during play and the printed manuals. The Players Guide which ships with the game is unbelievably bad, and I fail to comprehend how anyone could see it as acceptable.