Looking to resolve both of these issues.

How to get a call screening situation for multiple voip lines.

and how to get some sort of auto-ducking plugin for vmix.

any suggestions?

Call screening for voip lines will be external to vmix. You have two options;

1 - Use a hosted PBX service that allows you take calls into a receptionist or queue, put them on hold (or park them) then transfer them to the "studio" extension.

2 - Use a robust conference service. Some have similar capabilities. I use ZipDX, which has breakout rooms and the ability to move callers between rooms. You can receive the calls into a waiting room, move them to a green room, chat them up, eventually xfering to the studio.

Similar results, different approaches to the mechanics. Neither will be free, but they need not be costly.