Under sink noise

The water pressure may be too high and require draining. Also could be a drainage problem within the area.

Could be a macerator that’s malfunctioning or it could be a water boiler for hot water under the sink

hot water expansion tank under sink could be faulty / or there maybe leek on mains water pipe

The noise you're describing, especially with the presence of a "big white tank" under the sink, suggests it might be related to a water filtration system, a water softener, or possibly the under-sink plumbing setup for an unvented hot water system.

The loud engine-like noise and the presence of water in the walls, it's possible that there is a problem with your water pump or pressure tank. The noise could be caused by a malfunctioning pump motor or issues with the pressure tank's components. Additionally, the presence of water in the walls suggests a potential leak in the plumbing system, which could be contributing to the noise and causing further damage or this could be a water heater that is having problems with pressure buildup and nowhere to vent or possibly a leakage somewhere therefore always drawing water from the mains to heat.

Sounds like air trapped in the system. Bleed the system out and it should get rid of the noise