Do I need an OS in my device?
Will this device need an OS?


No device needs an OS per se. An OS simply provides an abstraction of the various operations the device is capable of; if these abstractions aren't required (e.g. the device will never change and will only ever run one piece of code until it dies) then an OS isn't necessary.


  What kind of parts are needed to implement an OS on such a device? (I understand this sub-question may be too broad for this forum, so I'll be glad if you can even me point to relevant literature on and off the internet.)


Definitely too broad. Take a look at Andrew S. Tanenbaum's Operating Systems: Design and Implementation, where he goes through the implementation of MINIX, an operating system for x86 machines.