Also have 2014 Luxury & can only offer advise from own experience.
1. Bad move on Lexus , you are right your I pod is in full view.
(A) Possible ideas, purchase long enough lead so I pod can sit in centre consul box.
(B) Favourite solution ( see topic "warning usb stick") download music onto micro usb stick (Amazon). Small
enough to leave in permanently with lid closed.
2. Side mirrors. You can only tilt up & down by switch on right hand side consul, fold is in same place. No automatic.
3. Keyless lock seems accurate 5 to 7 mtrs, 10 if clear line of sight to car. As far as I know no adjustment you can do.
Dealer maybe able to do something but previous threads have warned about cars unlocking from owners pockets although quite
far away.
Hope the above helps. Enjoy a different way of driving.