Yeah, it does. Cinebench does use some AVX instructions, and since you left the offset at 0, that's really demanding some extra power and voltage for stability.
As I said earlier, "At the same frequencies, AVX instructions need more voltage to run, draws more power, and thus produces more heat than the standard instruction set."
If you use an AVX offset of 2 or 3, you should be able to run with less vcore than you're doing now to get both stable.
As for the LLC setting being on Auto, it depends on how efficient the mobo is at it. HWINFO is one way to check how much voltage the Auto setting is using for Vcore.
There is a difference, and it's capacity. 300w of heat for 280mm, and 350w for 360mm.
Once the comfort zone of cooler capacity is met, there are serious diminishing returns on getting bigger, beefier, and more expensive cooling solutions.
For the 2nd part: only if you have no intention of dialing down on the AVX frequency. As you're already seeing, 280mm isn't cutting it with 0 AVX offset.