Is your CPU running too hot?
The 280mm Corsair H110 AIO radiator should work fine for your setup.
It should work fine. I don’t like automatic coolers, but they’re the bare minimum for your CPU.
Consider your needs and the conditions you'll face. A larger cooler can help if you're carrying more gear or need to stay cooler for longer.
Yes, if you intend to increase its speed.
You tested it without a cooler? That's impressive!
I made a mistake when setting up the APC first time; I didn’t realize I was damaging it.