I was wondering if there was a way to gather all mail (all Inboxes and all On My Mac) - say from someone or with some name in a title - and then put it into a folder on On My Mac.
Not automatically, no; at least no way I know of. Again, that could perhaps be done with an AppleScript or Automator action.
Mail Act-On might also be of interest.
The other aspect of the question should probably be done in a Filter to then catch all /new/ incoming Mail and send it to a folder. On this one, can I ask you if this Filter Folder can be in an Inbox or if it can be in On My Mac?
A Rule can redirect incoming mail to any mailbox you wish, whether it's on a server (as with IMAP or Exchange accounts) or a local mailbox.
Can I also ask you if there are any guidelines or tricks on choosing keywords, using quotes, or specifications for the Filter Search criteria? I /think/ that for my google Filter - that it started picking up any email that had any kind of google in the /full/ header of the email instead of just the title of who it came from if that makes sense
Try selecting "From" rather than "any recipient".
Regards.
Regards.