And, let's say I want to keep certain messages on MacMail but delete from my phone, how do I do that without going to the Mac? If I don't set up IMAP, then I have to bcc everything I send from my phone or iPad back to myself, right?
If by MacMail
means the Apple email application that ships with OS X and iOS and those accounts are POP the easiest, and perhaps only, way of saving the messages would be to do it on the Mac. In fact I am not even sure it would be possible to do on the iPad and you are on your own where the Android phone is concerned.
On the Mac using the Apple Mail application you would go to Mailbox > New Mailbox, select On My Mac
as the location and define a name for the mailbox then move the messages you want to save to the On My Mac mailboxe(es). Since On My Mac mailboxes are not associated with any email account you could then safely delete or change the accounts without losing the messages. However that does mean you would have to move everything to the Mac. Forwarding the messages from your other devices to the Mac is probably the easiest way to get them there. I'm not sure how your Bcc would even work.NOTE:
If you do go to IMAP accounts there is no way to keep some messages on one device and not the others except for messages you have moved to an On My Mac mailbox.
MBP, iPad and Android phone. Where do I start? Do I have to delete the accounts from each device first?
In older versions of the Apple Mail application it was possible to change an account from POP to IMAP or vice versa if the incoming mail server URL remained the same
but in the current releases it is not easy to even create a POP account much less change an account from POP to IMAP or vice-versa
. IMO the easiest way to go would be to delete the POP accounts and create new IMAP accounts.
FWIW I have my Mac, iPad, and iPhone set to synch Mail via iCloud. That means the Mail setup not the messages. So when I setup or change email on my Mac, that automatically changes the two iOS devices.