There is two parts to the generator on a dt and most bikes. There is charging coils that produce Ac current that the regulator/rectifier converts to 12v dc, to charge the battery. The 2nd is ignition coils which are used to produce a spark at the coil. Most bikes will run fine with out a battery, but with out the battery there to 'buffer' the voltage from the reg/rec you run the risk of voltage spikes so not recommended.
I presume the ignition switch interrupts the main power feed ( red and brown wires) and a feed to the ignition system, through the other two wires. I would see if the bike sparks with these other two wires (blue I think) disconnected at the ignition switch, but with the ignition on.

I've got a feeling the kill switch makes connection, grounding a wire to kill the engine. If you've got the two kill switch wires shorted together, that would be like having the kill switch in 'off' position. Also my dt will spark once or twice with kill switch in off position.

My understanding is the 1988 has the BN barrel and slightly longer stroke 0.5mm or something. 88 on wards they had slightly bigger bore and shorter stroke. Think if you mix and match parts you can end up with a 135cc or similar.

Being a 88 won't it have the longer stroke crank? With that and oversized 3mb barrel probably gained quite a few cc's

Normally it's 3 white wires coming from the stator to voltage reg.

Probably the cheapest option but I've no idea what the quality of them is like.

If the speedo works I doubt it'll be the cable, sounds like the speedo unit has suffered some damage, probably easiest to replace speedo unit unless you can find another spares one to cannibalize for parts.

I may have one, stripped all the starter motor parts off my engine. Can have a look if you want?

More mechanical advantage from a longer clutch activator arm maybe? Smoother cable routing?

I believe there expensive due to being a oddball size, something .5mm wide I think.