that it sounds like there is something up with the pump, possibly the machine just needs to be run heavily for a bit.  I didn't really hear cone hop but I do know they are louder with a lower water level as in your video.  You can check the cones by pulling on them to see if there is play in any of them, otherwise it's likely some excess play in the agitator shaft.

I never heard it named anything, but yes, my 1-18, on low water and no clothes, crashes and thuds on the downstroke, it's all water level related. Either use half a tub of water even for testing purposes, or throw in some clothes.

That squeal--I do not know.

There's a learning curve with 1-18's, but they are great machines, excellent wash, incredible rinse, fine extraction, just loud throughout.  It seems like a 3/4 load of clothes, water at only 3/4, is about the best turnover. Once your clothes get in that tall ring area as opposed to the close-set rings, turnover slows.

You'll have fun

The knock during agitation is sometimes caused by a worn or loose ball in the agitate arm. The squealing sound could be something in the pump, when the pump reverses and the foreign object will move away from the impeller in one direction and move toward it in the other direction. The other thing that would make an loud squeal on 1-18s was the rubber isolator in the motor pulley if it starts to slip. On the squealing sound I would just keep using it and if it is in the pump it may go away, if it is the motor pulley it will soon come loose and will need replacement. Be very careful if you try cleaning the rollers as if you get scratches in the aluminum rollers they will tear up the plastic urethane rollers, they are not neoprene as that is a soft rubber.

The acorn looking thing is a damper, it has rubber in it and is not intended to come apart, it sounds like you need to replace the complete agitate arm. These are of coerce NLA, but you may find one, I have good used ones if you want to contact me.