My Answers:
What is this assembly called?
Mechanical Clutch Linkage (duhhh 
)
What is the Y-shaped piece called?
No idea to tell ya the truth, I'd guess it has something to do with a ball joint bracket or something
What is the rotating bar called?
Z-Bar
What is the threaded post connecting the rotating bar to the clutch fork called?
Again, not sure, but I think it is called the Thrust Rod
The entire assembly has two cloth washers, what are they called?
Not sure about the official name, I found some at Home Depot in the plumbing section. Similar cloth washers are used in older bathtub faucets.
Where can I find replacement rubber rings and cloth washers for the Y-backet and other piece?
Again, found them at Home Depot. Just take in the originals (or if they are like mine, what is left of them) and compare until you find something similar, or the same.
I had to modify my cloth washers with a box cutter to get it to fit. Newer trucks had a nylon / teflon ring that you may find at a wrecking yard to replace the cloth ring with.