The 03 has the 5 speed, the 04 got the 6 speed. The steering wheel and armrest are in bad shape but if the rest of the car checks out you can always find those in a junk yard or ebay. The price is good IMO. Is that an aftermarket rear view camera?
Well did the PO replace the alternator or not because a bolt broke off in the block? That could be your problem right there if not. These engines can act funny after a power wash and it's been documented if you google it.
You stated that you cleaned the engine. How did you do it? Power wash or just wiping it down? If you used pressured water you might have got some things wet and just have to wait for it to dry out.
Forget about the phone it's old tech and will not work. You can't swap pioneer for the Nak system either without incurring lots of cost, The wire harness is different if I'm not mistaken.
Maybe you can ry cleaning them. This is a common issue as these cars age. Mines are weak as well.
https://www.clublexus.com/forums/ls-3rd-gen-2001-2006/566467-diy-seatbelt-cleaning.html
https://www.clublexus.com/forums/ls-1st-and-2nd-gen-1990-2000/272873-got-a-slow-seatbelt-get-your-1-tip-ready.html
https://www.clublexus.com/forums/ls-1st-and-2nd-gen-1990-2000/845023-lazy-seat-belt-2.html
https://www.clublexus.com/forums/ls-3rd-gen-2001-2006/566467-diy-seatbelt-cleaning.html
The defroster is part of the HVAC for the front windshield. For the rear window there's an electrical strip that heats it up. So which window are you having problems with? This actually sounds like a bad alternator from your description.
I like the way you think but I honestly would of just let them total it. You will never recoupe the money in upgrades and I think it was more of an emotional decision than a practical one on your part. We live and learn. I don't know about the other cars but the 01-03 LS 430 has a 5 speed and the 04-06 has a 6 speed which is sealed.