> 1. Will the above scenario works - using req\res from one environment(Env1) to another environment(Env2)
Yes, you can use RR pairs to generate a virtual service against any environment you like, assuming the application in Env2 behave the same as the one in Env1. Connection and queue parameters are provided when you generate the service.
> 2. As we are not planning for the recording, Do we still need proxy queues to be setup or can we configure these req\res pairs to the same live Queues in Env2 while "creating VSI from Req\Res pair"
You can omit proxy queues and generate your VS against the live queues. However, note that when you do that you can't run the original service on those same queues. It will conflict with the virtual service. Also, execution modes like pass-through, fail-over, and stand-in are not available without proxy queues.