Just giving you my opinions on these bikes, bearing in mind, the majority of them were abused.
Hopefully you got lucky, but the Sturmey were the pick of the bunch
How do I lube the rear hub ? Is it dropped through the spindle ?
If it doesn't have an oil port then the bearings are supposed to be 'sealed for life'. I lubricate mine by squirting WD40 down the spindle. It's fine enough to get in all the nooks and crannies when it's first squirted, then when the solvent evaporates it leaves a thicker protective film.
The front wheel has definitely been bounced up and down kerbs 😆 Fitted new spoke and trued it up as best as I could but the rim has been bent in places. Not to worry though, it still rides well and I’m not doing time trials on it.
The three speed works now after working out why first did not hold, it turns out the cable tab in the thumb shifter was bent and that lack of travel did not help the gear change. It’s got the same Sachs adjuster as my other Pashley but is marked SRAM
How do I lube the rear hub ? Is it dropped through the spindle ?
It shouldn't need 'lubrication' the units are sealed for life, yo probably do more harm than good, particularly the Sturmey Archer hubs, although the early ones had oil ports, the modern ones used a special grease, kind of luminous green snot!
Same go's for the SRAM / Sachs ,don't lube, it shouldn't need it
I take it you know how to adjust the SRAM/ Sachs gear, it's fiddly, the Sturmey is far easier.
I’ve just trial and error adjusted it. It all feels good now and I have a first gear
Yes, but without occasional lubrication the life isn't particularly long.It shouldn't need 'lubrication' the units are sealed for life,