The water flow in the first video!! Is that the hose from the transom assembly disconnected from the sea water pump? (< Pump intake side).
Are you using a garden hose or is the boat sitting in a body of water?
The info below is from Page 6A-5 + in the following link,
COOLING SYSTEMS - Boat Parts, Marine Engine Parts, Boat ...
Seawater Pickup Pump Output Test If an overheating problem exists, use this test to determine if a sufficient amount of water is being supplied to cool engine.
IMPORTANT: The following information should be observed before proceeding with test:
• BOAT MUST BE IN THE WATER FOR THIS TEST. This test CANNOT BE performed with a flush-test device and water hose.
• The ability of this test to detect a problem is greatly dependent upon the accuracy in which it is performed. An error in setting the engine RPM, timing the test or measuring the water output will affect the overall accuracy of the test and may produce misleading results. To help ensure accurate results, a shop tachometer with an error of less than 5% should be used. The boat tachometer definitely should not be used as its accuracy is questionable. A stop watch should be used to time the duration of the test to help ensure that the accuracy is maintained within one second. An 8 qt. (7.6 L) or larger capacity container calibrated in 1/4 qt. (250 cu. cm.) increments should be used to measure water output.
• Due to the manner in which this test is performed, it may not be possible to detect a marginal condition or a high-speed water pump output problem.
b. Belt Driven Seawater Pickup Pumps: (Bravo) Remove water hose, which runs between pump outlet and engine, and replace with another hose of same diameter, but approximately 3 ft. (1 m) longer. Hose should be wire reinforced or of adequate wall thickness to prevent it from kinking when performing test. Clamp hose at pump outlet only. Do not clamp hose at engine end.
2. Repeat test four times to check repeatability of results.
Alpha
Belt Driven Pump Output for 15 Second Period
7.5 U.S. Qt. (7.1 L) Minimum