Civilization – How much is faith worth

The money gained from performing a diplomatic mission is 350 + (50 * <era number>) where era number is just a serial number starting with 0 for the ancient era. In addition game pacing also affect this number: quick games modify this value by 0.67, epic by 1.5 and marathon by 3; or in other words:

             Gold in   Gold in   Gold in  Gold in
Era          Quick     Standard  Epic     Marathon
--------------------------------------------------
Ancient      234.5     350       525      1050
Classical    268       400       600      1200
Medieval     301.5     450       675      1350
Renaissance  335       500       750      1500
Industrial   368.5     550       825      1650
Modern       402       600       900      1800
Future       435.5     650       975      1950

I know of nothing else which can affect the gold amount.

Now, if I have a strong economy in the late game I typically gain another 100-200 gold per turn when in a golden age. That means that the only way in which a golden age is preferable to a diplomatic mission is when it lasts at least 3 to 6 turns. But usually by the time I get to the late game my golden age duration from great people is really low, and if you take into consideration that the influence gained is worth a few hundreds in itself, you'll see that a golden age looks less and less profitable in comparison. All this is especially true if you play in longer game speeds, which translate to higher gold.

Of course, golden age also nets production, so it's still a dilemma; but I do believe merchants are worth it from the financial aspect.

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... :)