To which values should I set the lang attribute of the html tag? (I have the hreflang set to x-default)
For the HTML tag, I would recommend using
lang="mul" as specified in the IANA Language Subtag Registry which stands for "Multiple Langages."
On the other hand, in regards to using
hreflang="x-default", I would follow Google's recommendations as described in the link below:
In which language should I write the keywords, title and description?
You should write the keywords, title, and description in the language of your primary audience.
For content that is in another language, you can encapsulate it in a
<div> with a
lang attribute set to the appropriate content:
Most importantly: is it relevant to optimize such a page? It will be shown only on localized version of google in countries with more than a national language
Yes. Consider the Wikipedia.org landing page. Wikipedia follows the same advice that I gave you above, and most people never have to interact directly with that page.