I wonder is there some setting in your global retroarch.cfg that your system can't handle? Have you tried backing up the retroarch.cfg file in your RetroArch folder and running RetroArch to generate a new clean config file?
Ah ok, I thought RA only displayed that if the MD5 checks out, I guess it only matches the filename then? In any case, here is the details of the MD5 details for the syscard3.pce file you need: http://docs.libretro.com/library/beetle_pce_fast/
Well, there you go. You more than likely have bad dumps then. You have the correct working BIOS as seen in your screenshot. You said in a previous post that they were working though. Look for Redump or Darkwater dumps, they are the best.
I'll tag @circo here as regards Emumovies.
In relation to a program to record in game videos, this will be coming to Launchbox as it ranked fairly high on the latest poll. In the meantime, I believe you can do this with VLC:
https://www.makeuseof.com/tag/record-screen-using-vlc/
I also use 4k Video Downloader to grab Youtube videos of games sometimes if I am missing some.
Let's focus on one platform, in this case TurboGrafx-CD. Can you show us a screen shot of your RetroArch, load the pce_fast core and go to core information. I want to see the bios is not missing.