How are you testing the headlamp washer?
They will only work with the headlamps illuminated (not just switched on auto) and only on the first pull of the stalk, after that every 5th attempt (on my RC anyway)
Yes sun lotion for tyres.. UV protection is part of many tyre gel brands offering. Well known in caravan and RV circles
e.g.
https://www.turtlewax.co.uk/products/wet-n-black-500ml
https://www.303products.co.uk/shop/303-high-gloss-tyre-shine-protectant/
Wheels are not routinely removed at service so it may be a chargeable exercise.
Is it worthwhile? Some suggest not as it may accelerate wear as new angles are exposed to the road and anyway if it does even out wear you end up having to buy 4 new tyres in one go?
Lexus Relax is the new extended warranty, it's not a service plan.
Relax gets automatically renewed at each annual dealer service. There's no extra charge for Relax but the service costs and any prepaid plan, are totally separate things.
Your handbook should tell you the procedure to adopt when rotating the tyres/wheels
Mine says to only change wheel positions with the power switch off and then to re-initialise the system, after checking the pressures are correct.