What are the recommended methods to clean huge PCBs like the one in the video?
Most soldering processes involve flux that must be cleaned from the board after soldering. Some fluxes are water soluble, so yes, using filtered water is fine. Most electronic components that can be machine mounted are washable. Buzzers often have stickers covering the hole to prevent water infiltration, and other components may have warnings or special requirements for washing, but generally most components are not damaged by brief exposure to water when not in use.
Other fluxes require different solvents for cleaning.
Typically the solvent, whether water or something else, is blown off the PCB and components after washing. Air drying may leave residue on the components, and exposes the various metals to water for longer. Heating may reduce exposure, but may still leave residue.
What happens to charged capacitors when water shorts them out?
Washing is done immediately after production, and prior to testing. Typically boards are not powered up until after the board is dry and clean.
If you need to wash a board after its been powered up, for instance after rework, then you'll need to discharge any capacitors and remove, cover, or otherwise meet the washing requirements of special components.
Solder joints do not get any kind of corrosion?
Solder joints quickly form a microscopically thin layer of oxide soon after soldering due to air moisture. This layer protects the joint from further oxidation and degradation. Water, over the short term exposure needed for washing, will not cause greater oxidation.
This layer of oxide is one of the main reasons to use solder with flux.
Is the antisolder mask waterprof?
Yes, typically it is.