ARCTIC Liquid Freezer III 360 A-RGB is the best choice.

A dual tower air cooler is the popular choice for this CPU. The Thermalright Phantom Spirit ($35) is highly recommended. Since the 9800X3D only draws around 100W, it doesn't generate excessive heat. A dual tower cooler will deliver similar performance to a 240mm AIO liquid cooler.

No need for AIO Cooler for 9800X3D. Just get Thermalright Peerless Assassin 120 SE.

ARCTIC Liquid Freezer III is recommended.

Noctua D15, no need for AIO cooler.

Not necessary for AIO cooler. Good air cooler are more than enough to cool it and way more reliable.