The input shaft diameter is the same all the way down the shaft (on a new input shaft). The reason it’s looser near the end is because the bearing interference fit in the past honed it down a teensy weensy bit.
You need the fit to be snug. (But not too tight). You don’t want the shaft to be...
Yes-
The input shaft pilot bearing is just tapped in completely dry.
Use a socket that’s the same diameter as the OUTSIDE bearing shell (race). You don’t want to apply any force to the inner central race.
I don’t remember what socket size fits, but one of them will be a perfect size.
Just tap...
Nobody (almost nobody) uses Toyota SSTs for anything except maybe the steering knuckle centering SST. Mostly because they’re not available and usually something else or a different method will work.
If that seal driver SST was used as shown in the manual to drive in the seal, it would use the...