Looking for free program that allows PiP, and cutting/splicing
Every Mac comes with iMovie. Every PC comes with Windows Movie Maker.  Both of them do cutting &amp; splicing. iMovie does one PIP at a time; you can't have more than one PIP onscreen simultaneously unless you do a workaround. I used iMovie for hundreds of short YouTube videos with LOTS of editing (and PIPs). I don't know whether Windows Movie Maker does PIP but I wouldn't be surprised if it did.

(edit)

Just Googled "Windows Movie Maker PIP" and found out there are free add-ins that do PIP. (At least there were for the Windows Vista version. I bet the current O.S. has add-ins as well!)