I need software that can help me create videos like this https://www.youtube.com/watch?v=UVezYxFEH5Q It should be cost-free and run on GNU/Linux. Also, I am very interested in dynamic zooms and transitions while the video is ongoingas you can see in the video.
The features you are requesting are common to almost all video editors... One known exception being avidemux (it is made for much simpler workflows).
For you request I suggest kdenlive (kdenlive site click here). It comes with almost all major distros and it is easy to start working with! Also great tutorials and examples on youtube and other sites, so worth a try...
Multi-platform, Mac, Win, nix.
Unless you need to integrate actual vision mixing hardware, there's nothing to touch it for free.
It's easily a match for Final Cut Pro & Premier.
…and, did I mention… it's free !!
The only downside is it really is jumping right in at the deep end. Expect it to take between two & six months to be truly comfortable with it.