Can't help with the first question, sorry.

But as for the second... I do this often.

Create a New Mailbox. Label it whatever you like. Move the messages you want to have on your other machine into this folder.

If you go into User/Library/Mail/Mailboxes you should see this folder. Transfer this folder onto your other Mac, depositing in the same place. Restart Mail. The messages you wanted to have on the second machine should be in this folder; move them around as required.

There may be other ways to do it, but this always works for me.

Good luck.