You can choose to autocalc a battle, either before it begins or at any point during it, which will immediately resolve the combat and determine losses. HOMM3 also has a separate combat mode, but it's turn-based on a hex map. Units move in order of speed, though you may have any unit delay its actions until after the others have moved. Unit values are affected by hero skills and artifacts, and certain ones allow you to redeploy your troops to different hexes before battle begins. When a unit is attacked hand-to hand, it automatically counterattacks once casualties have been removed, but most can only do this once per turn so that the effects of overwhelming assaults are represented.
Spells can be cast each turn by heroes - that's the extent to which they're on the battlefield.
There is an auto combat option which will let the computer maneuver your forces while you watch - this may be freely switched on and off. W3DLR and HOMM3 have many different shades along the warrior-mage axis. Skills are more specialized abilities. W3DLR and HOMM3 have stand-alone scenarios and campaigns of linked scenarios. Manual Pages is a bit misleading.