Best Practices

I'm trying to move emails from Apple Mail to an external hard drive. I followed the steps of clicking on my inbox, then selecting 'Mailbox' in the toolbar, and choosing 'Export Mailbox'. I selected my external hard drive in the popup window, but all that appears in the hard drive folder are two new folders: 'mbox' and 'table of contents'. When I try to open them, a popup says they can't be opened because they're from an unidentified developer. What am I doing wrong?

Additionally, I need to remove numerous old emails from my previous job from my inbox, but I want to keep them accessible in case my former colleagues need them. I'd like to transfer them off my current MacBook Pro before migrating everything to a new MacBook Pro that I've ordered.