Are clients permitted/expected/tolerated to run off and fetch the contents of image links for inline display, once a page containing such links is retrieved?
They are not supposed to do that, but some clients have an option to enable it anyway.
There are also clients that make a second request to ask for a favicon. In the spirit of the protocol the "icon" is just a UTF-8 symbol, but that behaviour is still controversial.
Only if the page is inside of a ZIP archive stored on the local computer and only if the link is to a picture within the same ZIP archive. (However, it would be good to have an option to disable inline display even in that case.)
Not really, in fact they're forbidden - those clients are spec-uncompliant.
Permitted? Technically, it can't be stopped (well, it kind of can, see "Tolerated?").
Expected? No, it's counter to the intentions of the community.
Tolerated? Maybe. Here's a fun one (saw this in one of the past discussions dang linked): https://github.com/makew0rld/amfora/issues/199. That was over favicons, but the response would be similar if linked images were automatically fetched. Though the protocol has a "backoff" return code that could be used to throttle those things that would be less disruptive than Drew's approach of banning specific clients.