I assume that both ends should be screwed out until they match closely the length of the one removed.
Once the ends are secured, I tighten the hex clamp (3), then tighten #1 against #2.
Therefore, to adjust toe, one would loosen the hex clamp (3), adjust, retighten #3 and tighten 1 against 2 again.
My current (old) tie rod has a larger nut where item 2 is on this tie rod. This new one isn't a nut at all, just a thick metal washer type thing. This holds purely by compression against the split, tapered sleeve, correct?
Not exactly sure what you are talking about here.
Personally, I would make the new and old tie rods as close to the same lenght as I can get and then take it to an alignment shop to have a proper alignment done.