Make videos still and stable?
You should be able to use any software for video stabilization. With ffmpeg you can use either deshake, or vidstabdetect/vidstabtransform. 

Depending on how shaky the original video is, you can get rid of the black distracting margins by zooming with the zoompan filter, or cropping with the crop filter. See the links for examples.

You'll probably have to experiment a bit to find out what works for your material. Use ffplay with the same syntax to see directly how the filters work.