What relation does narrowing jacket sleeves have to the height of the armhole?

Well I'm not a tailor but from what i can see no it will not. The armhole is a hole you can't really fill in blank space. Even if you narrow the sleeves the "hole" will still be in the same position. If you use the search function this has been discussed before and the consensus was that you can lower an armhole but you can't raise it.

Will have no effect on the armhole but may reduce comfort when you move your arms. Only way to make the armhole higher is by reducing from the top of the shoulders but then you have to recut the sleeves and shorten the collar, maybe lower the gorge. Kind of a big deal.

Don't know. Hard to say without seeing the jacket on you.

From my experience, as long as you are not slimming the sleeves too much, it will look alright, even with slimming you should feel comfortable to move your arms. If you did it too much the low armholes will look very weird.

as long as your not fat per say in relation to the armhole you should not find any discomfort.  Yes it be considered a slim fit once you raise the armhole.  Some folks try to make wear clothes like they have in when they are 250 plus pounds with 40% BF when im only 195lbs with 8%BF.....I need the higher armholes due to my slim physique.

Yes.

That's the area you don't want to touch or change. The sleevehead is cut very precisely to match the armhole and requires adequate fullness to hang properly. Once you change that, the sleeve distorts and you get divots and worse. If you are trying to spiffy up a conventional cut jacket to look slim, it won't happen.
Take the suit to a tailor and show him what you want altered and ask how it is done and if it possible. Extra cloth under your arms has nothing to do with the sleeves and since you are guessing what is wrong and what to do, you would be better served having a face to face with a tailor.