Do not use burned steels even though they are flat, as heat creates hard spots that won't friction evenly when they apply.
Absolutely replace that bushing on the drum, as that centers the drum on the stator for the sealing rings to center on the hub.
You definitely found hard rubber that causes "Morning Sickness" and no move symptoms.
The input shaft can stay on the drum, just clean all the nooks and cranny's.
That brown washer is exactly what you think it is and can be reused of it looks solid.
They are a little brittle, so don't tweak on it too much checking it.
From what I see you are doing fine.
OH, and if the rest of the pump looks that good there shouldn't be a problem reusing it.
Just put a new seal and bushing in it and don't forget to RED lockite BOTH the seal and bushing in place, and stake the bushing into the pump body.
Note that when you put the bushing in that you position the bushing seam 90 degrees away from the staking indents so as not to cause the bushing seam to open or disfigure.
I use a 1/8 or so drill bit and a ball peen hammer to stake the seal in.
This is the idea on the staking of the bushing, and after doing this I always fit it on the converter and turn it a bit to smooth of any high spots in the bushing.
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