Yes, this CPU cooler comes with thermal paste pre-applied. The NZXT High-Performance Thermal Paste is applied to the cold plate, making it ready for installation without additional steps.
If the fan is making noise, a bearing may be defective. You should be able to find the fan as a spare part. Simply unscrew the fan to see the type designation on the sticker and then search on digitec.ch or Google.
Yes, you can install the AIO water cooler in a Hyte Y70 case. The Y70 supports radiators up to 360 mm inside, which is sufficient for most AIO water coolers. Make sure that the radiator is not thicker than 30 mm to ensure that it fits easily.
You can place the previously applied thermal compound of the NZXT Kraken 360 RGB on your AM5 chip without any problems. The thermal compound is already pre-applied and ready for installation.