Free City

It's striking as if it were a unit, but it's still a site. Therefore, it won't die due to damage. It can still be destroyed by a specific destruction effect (e.g. Sinkhole), but it won't die due to taking damage.

Free City's ability is a passive ability that gives it the option to attack and defend 'normally' once per turn, as if it were a 3 power unit (while actually remaining a site). Therefore, it can only attack on your turn, and defend (presumably on your opponent's turn) when a unit or Free City itself is attacked by an enemy unit occupying Free City. If Free City would somehow have the chance to both attack AND defend on your turn, it can only do one.

The key word is 'here.' Clearly burrowed units are 'here.' Airborne and Stealthed units are also 'here.' But, to attack Airborne or Stealth, a unit needs some special ability (e.g. Airborne, Ranged, etc.) Since Free City doesn't have those abilities, it can't actually target Airborne or Stealthed units with an attack.

Since the ability to attack is granted by a card effect and not a basic ability, no tapping is needed, but it's still an attack. Therefore, players may declare defenders for the attack normally.

Yes, because only minions are subject to summoning sickness.

No, since the attack is not happening on Free City.