stepppy

If the LBX has buttons on the door like other Lexus models, then they are independent of the key and are programmed by setting your position, pressing and holding the relevant button to memorise the settings (until it beeps). Do that for each driver, then just press the button (briefly) when you get inside the car. 
I only use one key for myself and my partner as I like to have all the driving information under one profile. Not sure if two keys can contain all information in one place, but I have been happy with what I have set up. 

No, this is a mandated pedestrian safety feature.
"All new electric cars, hybrids and plug-in hybrids (PHEVs) must now be fitted with an Acoustic Vehicle Alerting System (AVAS), which will activate at 12mph and below, emitting warning sounds to alert pedestrians and other road users of the vehicles' presence."
Some cars used to let the driver switch off the warning sound (I had a Renault Zoe and it had a switch), but now they cannot be disabled.  Unless you want to invalidate your insurance and possible have someone with hearing loss walk out in front of you I would just get used to it.
My Prius, before my NX did not have any warning sound and I thought the noise from the NX warning sound would annoy me, but I quite like it now.  Luckily the NX has a speaker in the front and the back, so when reversing, the sound only comes from the rear speaker and is the same volume and from the front speaker when going forwards.  I believe some Lexus models now only use one speaker at the front and ramp up the volume when reversing which I have heard and can be pretty loud.

That is normal, it’s literally is just a message to check rear seats. 
This can be turned off in settings via the media screen.
It was one of the first things I did as I never carry rear passengers. 

I helped a friend move house this week and my NX spent a lot of time with the tailgate and rear doors opened whilst I loaded it with various items and I had no issues. 
After approx 10 minutes the interior lights automatically turn off just like several of my cars before it did.
Opened and closed the tailgate several times too. I did this about three times during the day and all was well. 
If I am sat in the car doing any changes to menus etc. I will always put the car in ready mode and press the EV button to stop the ICE starting, but I didn’t do that with the various loading/ unloading trips I did. I did have my jump pack with me just in case.
I am not sure why some cars seem to have issues and others do not. 
As it has been said many times here, anytime you are sat in the car using radio etc. always put it in Ready mode. 

It refers to the engine technology.
VVT = variable valve timing, the i for injection and I suspect the E is a reference to the hybrid technology.