For that to work you need to ensure good screening either by investing in CLs (too expensive) or spamming enough DDs that they will never end despite losses. Either way, DP secondaries are one of the no-brainer choices when it comes to ship fitting, because you need AA anyway (unless you can assure green air), so might as well stick to them for more synergy between ships. While you don't need to fill heavy ships with them, I find that having more than 3 heavy guns is overkill (both because of price and opportunity cost).
Chances are, in that case you'll be facing more capitals as well (at least, in case of AI that is programmed to use ships in certain ratios). Generally, battles go like the one attached (was mostly using stock ships, nothing fancy). While I did not kill any capitals, I was able to hunt them down later because they had no screening left (and AI insisted on putting them into action anyway). So even in "lots of screens" scenario you'll, at least, take their task forces out of commission for a while by simply killing off screens. Capitals (evan CAs) can survive quitre a bit of punishment and disengage, it's screens that usually die.
Because they are just mobile airfields, which is pretty self-explanatory? They can either provide your ships with fighter cover if you can't establish green air, or harass enemy ships (usually capitals) to varying degrees of success. Can be used as actual airfields in a pinch, but that's, usually, not a good IC investment. Pretty expensive (considering separate air research and production), so people rarely bother. Still, they can be used to pull off
Pearl Harbour, which can be fun (not for the receiving side, of course).
Basically, unless you need long-range power projection (read: not fighting in the Med/England), they aren't worth the effort.
(also, last I checked, carriers could not use their light attack, so secondary gun is kind of wasted on them)
