It's about 18" front to back, 14" left to right and about 19" tall not counting fittings. I'd say add another 3.5" just for good measure to account for the fittings if you use 90° fittings (obviously twice that much without the right angle fittings). It is not particularly loud. It is essentially a mini refrigerator or HVAC. It has an evaporator, compressor, condenser and fan. It's not quiet, but not obnoxious. No louder than your Nova fans. Probably similar loudness, but lower pitch sort of like a box fan on low fan speed. You know what your fridge or freezer sound like. Expect that in terms of how it sounds.
It puts out lots of heat on the exhaust, so put the back blowing out a window or out of your office door. It goes without saying you do not want the hot exhaust blowing into the radiator, as that would defeat the purpose of using chilled water.
I use a 5 gallon water tank wrapped in black foil insulation to normalize the water temperatures. It takes longer for 5 gallons to get cold but once it does the PC load while doing extended benching sessions doesn't really affect the water temperature that much. For benching do not use the radiator. It will heat the cold water and try to warm it to ambient. Just bypass it when benching.
For gaming you can use the radiator and the chiller together since you do not need to try to keep the temps as close to freezing point as possible. It will be a LOT cooler with chilled water even with the radiator, but the radiator will hold you back in a notable way when benching.
Yes, the Radeon hotspots are utterly insane. That is ultimately why I could not find any real love for the 6900 XT or the 9070 XT. Both were otherwise good GPUs, but the unfixable hotspot temps made it hard for me to like them. Even on chilled water the 6900 XT had totally asinine hotspot temps. Nothing I tried improved the hotspot temps on either of them in a meaningful way. AMD needs to find a way to address that engineering defect. Their product adoption rate would likely improve.