Great,
It seems iMX28 is a good fit for you. I highly recommend it.
As for the supply question, you are right, you just need the 5V input, additionally you could use a high-capacity battery input and/or a coin battery input for the RTC.
As for Kinetis MCUs, they cannot run Linux as they don't have a MMU, they can run uC Linux though and many RTOS available in the market, in case you want to explore that more, per your features requirements, I would recommend K60 in 2 different versions:
K60 100MHz - will give you everything but the 400MHz, DDR and NAND controller.
http://www.freescale.com/webapp/sps/site/prod_summary.jsp?code=K60_100&nodeId=01624698C9DE2DDDAF
K60 120MHz - gives everything you require but the 400MHz.
K60_120 Product Summary Page
As for RTOS, as Carlos already mentioned, Kinetis comes with a +15 year old commercial, free of charge RTOS, called MQX, that also includes Ethernet, USB, File System and IO drivers on the same package, the full-featured basic package is free for use with Kinetis MCUs.
Freescale MQX™ Software Solutions Product Summary Page
There are specific forums for those solutions, you may want to take a look:
MQX: MQX Software Solutions
Kinetis: Kinetis Microcontrollers