Try a safe boot, power up holding the shift key, hold the shift till you see the progress bar, login take a look, log out and restart normally. (This boot will take longer than normal)
Also try highlighting a mailbox in the side bar of Mail and from the menu bar click Mailbox, at the bottom click rebuild mailbox, if that helps try the rest one at a time.
Never heard this one.
Hope it helps, but it should not harm anything.
All the best