Request: Mark string as "translation is not necessary"

This sounds like fixing upstream software, IMHO.

If you believe string should not be translated, please inform the upstream developer of that, so they can unmark it. With that, you'll get all those benefits you mention: you won't see them among translations, they'll be dropped out of statistics, etc.

Ok, with the software I can contact upstream devs.

What to do with documentation? If I understand correctly, documentation (like all kind of guides) is handled separately. Whom should I contact then?

I agree with danilos. If some string shouldn't be translated at all, for any language, it shouldn't be marked as translatable in the original version of the software.

I don't understand what you mean with documentation, though.

If rosetta offers documents for translation via PO files and some strings aren't meant to be translated, we have the same case here: the document should be fixed, or the tool generating the po files enhanced so it's possible to leave stuff out.

Exactly. Documentation would need fixing itself as well.
Marking as "rejected": if you have any other input, feel free to also reopen.

I think there should be an option to mark GUI strings vs. terminal/command line strings.

For example, in the Hebrew translation group we decided not to translate terminal/command line strings for now because BiDi problems and because people will have difficulties finding support (Google, forums, etc.) if the strings in terminal will be translated into Hebrew.

But there isn't an elegant way of knowing which strings are GUI and which are in terminal.