Civilization – Barbarians spawning even though barbarians are turned off

All percentage bonuses are live and recalculated whenever the affected value changes, which is to say they are always based on the current base value, and not any historical value.

Since it's the given example, lets look at the +33% bonus to great person generation from the Hagia Sohpia.

Let's say that initially you have a city producing +3 great engineer points, with no other percentage effects currently in place.
You then build the Hagia Sohpia.
The +33% from the wonder will be applied to +3, boosting the output to +4.

Then, a few turns later, you adjust the citizen allocations for this city so that the base rate is now +6.
The +33% from the wonder will be applied to +6 (the current value), boosting the output to +8.

I believe that all ground units that are air-intercept capable can protect in a radius 2 hexes around them. According to research done by Oak, air units can intercept anywhere in their attack range. A single ground or air anti-air unit can only intercept once per turn. Interception does not guarantee destruction, and it's possible that your unit will still be injured or destroyed even if the intercept is successful.

My strategy when assaulting a naval stronghold such as this is to bring overwhelming force, and plan to lose a few units. (This strategy would certainly be historically accurate...)

If air units are an issue, are you bringing in adequate ground-to-air (and/or sea-to-air) defenses? Carriers can store fighters that can intercept enemy fighters attacking your land and naval units.

I would suggest setting up some carriers and other ships to protect your embarked land units from enemy air and sea units while they get into position. It's not 100% clear from your question, but you are aware that you can attack the city while embarked, yes? Otherwise you've got another turn delay where your unit is vulnerable when you disembark.

As I suggested in the comments, I'd also consider choosing a different tactic or priority target if you can. Small 1 or 2 hex island cities aren't generally high value targets, and their production pales in comparison to a city near forests and hills. Plus, they're hard to assault (as you've noticed) and if the map isn't all islands, fighting the brunt of their forces in a sea/air engagement by building a bunch of ships you don't have a use for once you capture the islands might not be the best use of your military resources.

If you can bypass these islands, you might be better off capturing some of their higher value cities inland, thereby crippling their war machine. Who knows, they may even offer you the islands when they beg for peace... :)