IanML

If I read the linked message correctly, the whine was allegedly from the transfer box, for which the recommended grade is 85W90, and the substitution of 80W90 the cure. Have you done that, by any chance?

Before you do anything drastic, have a read here. Apparently, the transmission whine can be addressed by a lighter oil. I have the same symptoms, and I think it's worth a go.

You can't pass the MOT test in UK if the DPF has been removed.

Assuming you have wired a switch to control the relay, with the switch in the off position, put the meter across the relay contacts (the supply and the lead to the lamps). If you measure battery volts, the relay is "off" (the contacts are open), and your led's are picking up power from elsewhere. If you measure a small voltage or zero, the relay contacts are closed, and you should now disconnect one of the control wires from the relay and measure again. If you get the same result, the relay is defective (contacts are permanently closed); if not, the control wires are keeping the relay on permanently, and you need to investigate whether the switch is defective (contacts always closed) or there is a short across it.

On the general point about spares for older models, if unavailable in UK, a good site to try is Amayama. They have a large warehouse in the UAR, and will air freight to UK. Not cheap, but if you're stuck....

On the parts diagram, it looks like the motor is centrally in front of the roof aperture.

67881-42030 Weatherstrip Back Door. £125 on EBay

I have the same car as you, but mine is whisper quiet unless the engine is working hard on a hill. My rear door is quite resistant to being shut, so I would guess yours has either lost the rubber buffers or needs the striker adjusted.

You need Toyota Techstream, e.g. here.

Here you go: https://smile.amazon.co.uk/SYNTHETIC-80W90-GEAR-LUBE-32OZ/dp/B000RZSJJM/ref=sr_1_1?ie=UTF8&qid=1545684194&sr=8-1&keywords=80W90+synthetic

Try lubricating the steering column universal joint (just above the rack).

Sorry, but that is wrong. The alternator is capable of supplying all the car's electrical load, and, simultaneously, replacing the charge in the battery which was used when starting. Even if the alternator is developing its full rated current, it will not cause the engine to stall.

Page 303. Having read the limitations of the EV Mode in the manual, I have to say I'm not very impressed. All that complication for very little benefit. Not for me!

1 US Gallon=0.833 Imperial Gallon, so 33 US mpg = 40.8 Imp mpg