I don't see any relay in the schematic. Is the LED taking its place while you develop the circuit?
The 555 appears to be wired pretty much right, but I can't tell if it will do what you want it to do, because I am not sure what it is you want to do.
Take these two of your specifications:
I want it to when the 4n29 is powered the relay stays “as is”
When the 4n29 is UN powered I want ~ 3 minutes to go by and the relay changes state.
When the 4n29 is re-powered the relay goes back.
How will the 555 know whether it is the first time the 4N29 is powered or the second, third, fourth, etc. time? Is there some time-off period after which when the 2N29 is re-powered, there would be no change in state? Are you simply looking for a latching circuit?
As for the 4N29, it is permanently in the circuit, so I assume by powered and unpowered you are referring to its LED emitter.
My best guess is that you want the 4N29 to control the delayed operation of a relay driven by a 555. Can you expand a little more on what you need (i.e., the bolded text in the quotes)?
John