What you have described is how an RPA would work and should be setup. Keep in-mind that the RPA execution isn't instantaneous, so your user should be done with that take stage of the case for the time being. They may get the case back in their queue after the bot has completed, but depending on how much work is in the bot queue at any given time, the case might not be worked immediately.
1) Our requirement is to have the automation to run in parallel with the main flow. In that case, can we have a Parallel Process in a Stage and there we queue the Case to Robotic WQ?
2) Once any Automation is completed say Case A-1, it will be marked as completed and still be present in that Queue which will delay the execution of another automation of say Case A-2? Should we do any action further for the case to come out of queue?
I believe you can use a parallel process here, but you might want to test this out as this is not something I have ever done.
Once the robot picks up a work assignment, that work is no longer in the Robotic queue. If this case needs to be worked by a different robot later, then it would need to be placed back into the robotic queue for another robot to work.