The "huge pile of washers" is not "wrong" functionally so much as untidy. Yes, some neat new spacers would be welcome there.
I am pretty sure you can service that detent without removing more than the handle.
That gearbox can trip you up. It drives both the feed-shaft and lead-screw and whilst it can help extend the possible thread range, the one you cut will agree with the change-wheels alone only if the gearbox is in the 1:1 ratio.
(What do you mean, how do I know?)
On the other hand, you can use it to co-operate with suitable change-wheels to set a super-fine self-acting feed for finishing cuts.
Verify the actual spindle pinion tooth-count agrees with that given on any screw-cutting tables you have for the machine. On my Harrison it seems fixed and not changeable, and is not the one quoted so I have to calculate the wheel-train each time.
;;
A tip to help you keep the lathe clean. Obtain an oddment of standard, round PVC rainwater down-pipe, cut two pieces; one the full length of the headstock, the other ditto the box part of the bed at the tail end. Cut them lengthwise to form two "gutters" slightly under their radius, in depth, to a gentle push-fit under the shears below the two stocks. They stop the huge voids in the bed from filling with oily swarf, and direct any oil leaking from the headstock into the chip-tray.
For sweeping out the chip-tray on both the Harrison and the Myford lathes, I use old paint-brushes, with a child's plastic toy beach-spade about 8" long as a "dustpan".
(Oh, and I tend to use the tail-end PVC "gutter" on the L5 as a handy little temporary tool-shelf, too! 