quarantine 'em

The second question is easy. Inspect the "Accept-Language" HTTP header, serve the page in the most preferred available language

But in this case, we would have a situation where, like, five out of the 655 pages on my site randomly appear in Hebrew, the rest in English

This would be very surprising behaviour, and not terribly helpful to someone expecting to read the whole story in a single language

Or even to someone expecting to browse the whole site in a single language

I know for a fact that it's not acceptable to, due to incomplete translation work, serve one web page in a mixture of languages

Accept-Language is only good for discovering the default, you ought to redirect to /en/ afterward

If I'm going to redirect to /en/ afterwards, why inspect Accept-Language at all?

To determine the user's preferred default on a first visit.