RE350 and RE450 could be set as an access point, at the top right corner of the configure page there is a setting option "mode", click this option and you will be able to set the range extender as...

seems that you have problem resetting the device. you could refer to this FAQ: http://www.tp-link.com/en/faq-202.html if you still have problem, you could have a try to contact tp-link local support...

4220 could work with 4226 KIT, they follow the same technology and protocol

How did you do the ping test? From the laptop, you ping the Lexus? or From the Lexus, you ping a host on the Internet? Or, from the laptop, you ping a host on the Internet?

You tried other phones and are just working fine, as long as smart TV and laptop. I think this may be a compatible problem, between nexus 4 and this router with messaging apps. To further locate this...

I have contacted the support of TP-LINK, they said a new firmware for TL-WA801ND V2 is coming, let's see this firmware will handle this issue. Cheers