I know of no way in which MEP could do what you want. Essentially you need to simultaneously record two sources, the feed from the person you are calling and the feed from your webcam. In effect, this thus becomes a "multicam" project, not possible "live" with any Magix product, I think.
. . . . Does Movie Edit Pro record video calls . . . .
In theory, as the conference call will be in a windows on your computer, MEP should record, ie screen capture, the video conference.
Testing with Youtube video it works.
There is a legal issue you may need to address and that is informing the other person(s) that you will be recording the call and get their consent beforehand - preferably in writing or email.
In many countries it is illegal to record someone without their explicit permission.
Try a capture screen software like Snagit or Camtasia Studio or Screen-o-matic to recrd all on your screen and create a video after you can édit the video.
Thanks John. I just want to record my screen with my picture in the bottom. So as I'm teaching, people can see my slides or video as well as see me talking. I'm not interested in recording others who are on the call.