I've noticed that "animating with mouse" has become an animation style of it's own on youtube recently. Mostly in comedic contexts which does look quite charming but in education videos as well which seems to be very functional.
An easy way to achieve this style in video is to fire up gimp (or some other image editor) and hide cursor in the recording software.
This meme[1] is pretty famous but doesn't hide the cursor or anything. There are a few others like it, I've never seen an educational video done like that though
How do they manage to move multiple “cutouts” independently at the same time, using the mouse? Especially when they’re overlapping. Green screen multiple recordings, and then merge them? Or is there a simpler explanation?
Yes since the background image is static you don't need a greenscreen. From watching just once, I think the guy never overlaps his clone(s). So you make two separate versions where their bounding boxes won't overlap (requires some planning) and then just show the left two-thirds of the bg image with guy 1, and the right one-third with guy 2, divided by a simple vertical cut.
And the overall zooming/panning is done after the merging. That's how I'd approach it.
An easy way to achieve this style in video is to fire up gimp (or some other image editor) and hide cursor in the recording software.