Is it possible to make animations on SketchUp Free? Is it possible to export them to MP4 or WEBM video?

I’m using the Sketchup Free plan.

Not very straightforward, but you might get what you want by this method.
To export the animation to MP4 you would have to use an application to screen-record it and then export the video recording.

(Sorry for the bad quality, had to reduce file size to be able to import it here)