Note that Firefox doesn't use Qt, so that illegal instruction error should only relate to the VLC issue.
I don't play video in Firefox, but I believe to do so it uses libavcodec, which isn't loaded by default.
Try loading libavcodec5.tcz:
tce-load -wil libavcodec5
It could be that other extensions are also required, and if using the Mozilla binaries via the firefox_getLatest.sh script, you'll also need PulseAudio for sound (with firefox-ESR.tcz you only need ALSA).