Yes, for any attachment/mime-section ("inline" is just a flag of "Content-Disposition" header in corresponding mime section).
No, across many emails, at least not without writing some macros.
Sort-of, labeling deleted attachment. You can attach a label to whole email, or edit raw, to edit/replace an attachment with placeholder/label text. A bit fiddly, but doable with some vim-fu.
I've just tried doing this with Mutt. It's quite awkward, but (after fidling with the interface) it did create a new email with an empty attachment, i.e. the attachment is still there, but it has zero bytes. Also, the original email remained within Gmail. So, it seems that Mutt doesn't work well with Gmail for this use case. (Disclaimer: I am the author of the web app Unattach.)
That's a "feature" of gmail's IMAP server that is easy to confuse for a client bug - see pugio's comment about having exact same problem when using Thunderbird.
Gmail knows nothing about folders (where given email is in exactly one of those), instead using "labels" (which an email can have zero or more of). Problematic "feature" here is that their IMAP interface exposes labels as folders. So, if client asks server to delete message from given folder, instead gmail removes label with that name (then adds "Archive" label, to confuse thing just that little bit more)
Luckily, there is an obscure "When a message is marked as deleted and expunged from the last visible IMAP folder" option to rectify this intentional defect.
No, across many emails, at least not without writing some macros.
Sort-of, labeling deleted attachment. You can attach a label to whole email, or edit raw, to edit/replace an attachment with placeholder/label text. A bit fiddly, but doable with some vim-fu.