Why did the oxygen run out in FTL

As always, the best defense is a good offense. If you can take his drone control offline, you just need to work harder to keep it offline. That might mean targeting the drone system to disrupt repairs even when there are other undamaged systems to target. You are correct that drones can come back online quickly and this is an issue. I'm not sure the enemy actually has to spend drone parts to do this, though you would have to.

Defensively, dodge and shielding of course matter. You can't have too much of either (well, dodge from engines experiences diminishing returns at higher levels of system improvement, so don't overdo it there). Getting to 2 points in shields fairly early can be a very good investment, and I like to have 3 by sector 5 or so.

You can destroy drones around your ship with ship weapons, however this is a coincidental thing and the drones can be brought back online with the expenditure of a drone part. If the orbiting drone happens to collide with a projectile, boom. It's very unusual; I have only seen it once myself.

Ship upgrades are not what enables you to win against the Rebel Flagship, equipment is (which requires some upgrades, of course).

And your equipment just isn't good enough. You don't seem to want to hear it, but ion weapons are difficult to use against strong shields (and not much use at all when you can't keep up a constant barrage) because they don't remove enough layers for the weapon slots and power they use. You write:

Ions are the only way of keeping a ship's shields down once they're down with the Engi cruiser, and they're the only tactic I can work almost flawlessly.

That sounds like you haven't tried enough burst lasers. The idea is to punch down the shields and still have some shots that actually do damage to the shield subsystem, such that next time there will be fewer shields to punch through. Things that can help with this:

• Bombs or missiles to weaken the shield subsystem (bombs are better because they can't be blocked by a defense drone) before using the lasers
• The weapon pre-igniter augmentation gives you a free shot
• A fully experienced crewmember operating the weapon controls and the automated reloader augmentation speed up weapon reloading to give the enemy less time for repairs
• A cloaking system protects you better than anything else