The heading "Global", shown when searching from the index on help.libreoffice.org, is not translatable.
True, but none of the other names too because they are the modules names...
The other modules expectedly so, as they are proper nouns - unlike "Global".
It must be localizable, yes.
Ilmari Lauhakangas committed a patch related to this issue. It has been pushed to "master": https://git.libreoffice.org/help/commit/df6f47ebcb1caf2a9791661de0fa8c484efd0515 tdf#129697 Use LIBREOFFICE instead of GLOBAL as index heading
Now it does not need to be translated.
Yes, but it hardcodes the product name.
Ilmari Lauhakangas committed a patch related to this issue. It has been pushed to "master": https://git.libreoffice.org/help/commit/919def267b89cfe03f40218baa8c16cf65526448 tdf#123318 tdf#129697 Don't hardcode product name in CSS and JS