I'll try breaking it down and going slow:
CV Main/Teacher, yes. Not sure what you mean by reaping benefits?
Correct. The "AA on one side of the ship prioritizes the other size for a time." So one side weakens while the other gains in strength while the Priority Sector is set.
It used to be a "fire-and-forget" version which you'd set and then have to toggle if you wanted to change it. Currently, it's on an Activation system where it boosts the one side for a time.
Yes, it may very well be unknown to players. I've made videos about the skill personally, but my videos are not standard and I don't believe we have a "How It Works" video that formally describes the Priority Sector mechanic.
Worth knowing that when Priorit Sector was altered in Patch 8.7 to the current version, it gained "Instantaneous Damage". This is damage which is applied instantly to all squadrons that are in AA range on the activated side. This damage is not insignificant and is a great reason to use Priority Sector even if you are concerned about your AA being strong/weak.
While this juke is possible, most players tend to pull their ship over at least a bit to keep the Sector'd side relevant while being attacked. Also, the continuous damage can yield more damage than you'd lose to the crossover effect on ships with middling or poor AA, so it's better to learn to use the skill then avoid it.For someone actually putting 2 points into the commander talent, hopefully they'd known what Priority Sector is/does.
...huh?
I don't know where this number comes from. Are you talking about Instant Damage?
DDs do 5% Current HP, CA/BBs/CVs do 3.5% Current HP.
On a 9 plane squad that is full health, the Instant Damage would do:
45% of the 9th's Plane's HP if a DD used Priority Sector
32.5% of the 9th Plane's HP if another class type used Priority Sector
If the squadron is damaged or missing planes, the Current HP will be lower so the Instant Damage will be less.
You're wondering if it's "worth it" to use Priority Sector on the initial strike run? The answer is going to be yes.
Use it at Max AA Range, because as the Sector heats up it'll help out your Mid-Range AA. Long-Range AA is usually small, so having the Instant Damage applied and then making the Mid-Range be more effective is the most impactful way to use the skill.
Flying is from 5.8km AA to strike is usually about 5-8 seconds, so the majority of the Sector is used in that. There's a few seconds of "slingshot" which will stop the rest of the damage. After that, the CV driver will assess if they have the plane resources to turn around and strike again.
If you've used Priority Sector and killed 45% of a plane, then your AA should finish the wounded plane and damage (or kill) another. The CV driver will feel out your AA off the initial strike, so waiting for a post-strike Priority Sector will actually encourage a follow-up strike. While you might do this as a form of AA trap, the best defense against the CV is to bloody the nose of the planes and encourage them to bail post-strike and take the time to fly back.
You don't have to take your guns off target. If your guns are sighted on your enemy, you can hold Right Mouse Button to Freelook. While in this mode, you can keep shooting and your guns with retain the same "lead" on the target. Obviously, if the target adjusts their course/speed you'd need to update the firing solution, but for something as quick as looking over your shoulder to pop Priority Sector you should be fine.
Priority Sector in Patch 8.7 was a way of giving players "Manual AA". Obviously, it's not the engaging mini-game of manning a gun and shooting down planes... but you can see how hard it is for most players to stop what they are doing mid-fight just to look in the direction of some planes and click a button once every 20-30 seconds. It's minimalistic, but that because combat can be so taxing.
You're hoping for like... an explainer of what Priority Sector does in the skill description on the Commander Screen? Just putting +25%/-25% would be confusing if people don't have reference. For those that know they skill, they should already understand what that means.