Isolating Digital IO from Microcontroller
I want to Control the Relay using the 24V tapped from the input of
  Non-Isolated DC DC converter. Does this configuration provide
  Isolation? 


No it doesn't provide isolation because it bypasses the isolation provided by the opto-isolators. However, if you can rely on coil/contact isolation then you have isolation but, that then begs the question as to why you are using opto-couplers to drive relays.


  or Should I use only the Isolated 3.3V to control the
  relay? (which won't catch relay startup voltage)


Try making your isolated DC/DC converter more like 24 volts or 12 volts and have this power the opto AND the relays. If you need feedback signals to the microprocessor then that might be a good reason for the opto-couplers.


  Since I have potential free Inputs, I can use either ground or
  positive voltage to sense the NC contacts of a relay. I think the 24V
  tapped from the Inputs will provide long distance sensing proper. But
  what happens to the Isolation?


You lose isolation - if you want to feedback relay activities to your micro you need isolated feedback circuitry (maybe consider using the ADuM5401 range from ADI) or use the opto-couplers but you need an isolated supply to the relays: -




  This device will be DIN Rail mountable. If I have to use chassis
  ground, which ground should I share with Chassis ground? or is it even
  necessary as we will use only plastic enclosure?


If you were to use any external ground it has to be connected to your microprocessor ground for at least EMC reasons I would say. After all, your output relays are isolated and this means they are also isolated from ground unless wired that way in certain applications of your module.