Can an Aerial Hero capture a Stronghold by beating its score ?
No. No aerial element can capture a Stronghold by itself, unless the total score of the stronghold is half or less that of the attacking element. Non-aerial elements capture a stronghold just by beating its score. Note that combat results are calculated based on the most dangerous thing in contact with an element, not the element it is actually fighting. Thus, if an Aerial Hero attacks a Stronghold, supported by a Horde, the Stronghold will fall if it loses the combat. Although it fights the Aerial Hero, the Horde is the most dangerous thing in contact with it, as a losing Stronghold falls to any non-aerial element in contact.