Okay, so page 18 of the rulebooks states that if there are no defending units, the attacking player automatically wins the edge battle. However, what if the defending player declares one or more units as defenders, the edge stacks are formed and revealed, and due to the effect of one or more Heat of Battle cards, the defending unit(s) are destroyed? In that case, do we continue resolving the edge battle as normal, or does the edge automatically go to the attacker?

Since the edge battle has already started, it will continue to its conclusion. But the attacker /will/ be receiving the I opposed bonus, barring any shenanigans on the part of the defender. (It's a trap!)

I was wondering what happens if you declare an attacker that has icons that depend upon you winning the edge battle and there is no defending unit.

If I have Obi-Wan Kenobi as an attacker and Ackbar as an attacker and my opponent has no units as a defender will I get to place 4 focus counters, 2 from Kenobi and 2 from Ackbar or will I only get to place 1 Focus counter?  We came to the conclusion that sice the rulebook says you auto win the edge battle when there is no defender that we still get those icons.

If no defenders are declared, the attacker automatically wins he edge battle.  So yes, edge-dependent icons would be active.