Yes, you can start another AOS process (with all the applicable fees) when your CN becomes current.
No, the beneficiary cannot start any part of the process until after you the PA complete the AOS process. Then you'll initiate the process for your case file to get transferred to the home embassy of where the beneficiary is residing to undergo their own interview process. Beneficiary cannot be approved or interviewed without the PA successfully completing the process first.
I have another concern. I talked with one lawyer. She recommended doing interfiling my old I-485 explaining that I have another option (DV-lottery) plus my employment based petition. What's your idea?