THE ABSOLUTE FIRST THING YOU NEED TO DO IS REMOVE THE CARBURETOR AND RE-INSTALL THE ADAPTER PLATES WITH NEW GASKETS AND SEALER!!!! as Mitch has already mentioned.
YOUR CARBURETOR IS LOOSE AND SUCKING IN AIR AT THE BASE AND/OR THE ADAPTER PLATES!!!
NO AMOUNT OF CARBURETOR ADJUSTMENTS WILL DO ANYTHING TO FIX YOUR ISSUES, UNTIL THIS IS DONE!!!
AFTER you do this ^^^^^^ then follow the instructions below. After watching the videos you posted above, where you could MOVE the carburetor with your hand........it's fair to say that right now, your carburetor is completely out of adjustment! You cannot have ANY movement in the carburetor like you do currently!!!
This pertains to the WEBER carb only:
1) Start the engine and let it warm up.
2) Rev the engine once or twice, and make sure the choke flap is in the vertical (OFF) position.
3) With the engine idling, remove the vacuum hose from the distributor.....there should be NO vacuum on the hose!
4) There should also be NO change in the idle speed after doing this!
If there IS a change in the idle speed (up or down), then the IDLE ADJUSTMENT SCREW is turned IN (tightened) too much!!!! You will need to back off the IDLE ADJUSTMENT SCREW (loosen) some, and adjust the MIXTURE SCREW to compensate.
As the IDLE ADJUSTMENT SCREW is tightened down, it will OPEN the throttle plate, inside the base of the carburetor. The throttle plate should only have to be barely cracked open for the engine to run/idle. If you have to open the throttle plate more than 1.5 turns from the point where the screw tip contacts the throttle shaft (with the choke flap in the vertical OFF position), to get the engine to idle.......then something else is out of adjustment!!! Usually that is the MIXTURE screw.......unless there is a vacuum leak somewhere......like at the adapter plates. In rare cases, the carburetor may have too large or too small jets installed in it for the engine's cubic inch size that it's mounted on.