I don’t have an Endless device at hand right now, but this looks like it could be an issue with the Internet browser itself, in which case eos-fix-ostree-repo wouldn’t do anything to fix it.
Reading through your diagnostics file, I see you’re using a fairly old version of Endless (3.3.14), which comes with a fairly outdated version of the Internet browser, based on Chromium 64 (current version is based on Chromium 69), so it’s perfectly possible that the problem you’re experiencing is caused by that (using an old browser).
I also see you don’t have any other browser installed, so my first recommendation would be for you to upgrade Endless OS to the latest release (3.4.8) which, besides lilkely fixing your issues with YouTube and Facebook, will also incorporate many other updates, bug fixes and other improvements throughout the whole platform.
Alternatively, if you don’t want to update the whole OS for any reason, you can try to install Google Chrome from the App Center and try playing YouTube from there, since that way you should get an up-to-date browser too (Chrome is not tied to the OS as the Chromium-based “Internet” browser, so you’d get Chrome 69 that way). Or even Firefox, which I believe is also available.
Hope this helps,