Will this kit run at 6,000 MHz on my board?

It runs at 6,000 MHz when the motherboard and CPU support that speed and you enable XMP (Intel) or EXPO (AMD). On weaker memory controllers you may need to drop to a lower speed or tune manually.

Is 32GB in two sticks better than four sticks?

Two sticks put less load on the memory controller and usually reach higher speeds more easily. They also leave two slots free if you want to add more later.

Does it fit under a large air cooler?

The heat spreaders are taller than bare sticks, so check clearance against your cooler's fan and fins. Low-profile coolers and most AIO liquid coolers are not an issue.

Does it work with AMD AM5?

Yes, on AM5 boards that list 6,000 MHz DDR5 support. Enable EXPO in the BIOS to run at the rated profile.

Is this kit worth it over a slower DDR5 set?

For gaming, 6,000 MHz is a good balance of speed and stability, and the gains over 4,800–5,200 MHz kits are real but modest. Buy a slower kit only if your board or budget limits you.