sedges

Just after some assurance from those with deeper skills and understanding before I jump into this and start ordering parts.

I am replacing cranks/chainrings on a 1992 Trek 820. I was hoping not to replace the BB, but when I pulled the cranks to measure the spindle and BB shell it was obvious that the bearings are in rough shape. Not loose, but growly. Also the spindle is 122mm( I guess 122.5) and I don’t see anything that uses that for sale.

I am trying to maintain chainline with middle chainring 50mm from centerline.

I am replacing Shimano Biopace 48/38/28 and square taper BB with 122.5mm spindle in 68mm shell.

With

Shimano Alivio FC- M410, 42/32/22 square taper and recommended
Shimano BB UN 54 68/118.

I am assuming the recommended 118mm spindle length is to maintain typical 50mm center ring chainline. Am I right?

Are my assumptions correct? Is this going to work?

Am I crazy not replace cassette and chain at the same time? I think I can still get a 7 speed cassette to fit.

Thank you for your help. People on this board are amazing!