If I attack from an adjacent enemy home territory hex and then empty it DURING THE BATTLE by taking reinforcements that hex is still 'mine' for the duration of the battle, right? So if I decide to retreat back to the now empty hex the retreating units do not lose a step? This because hex control is checked after movement and then after each battle, right?
Yes, that is correct, as long as you own the adjacent hex at the end of movement. leave some cav, garrisons, leaders in adjacent hexes, for controll.
FWIW, retreating from a skirmish to enemy territory is costly.