I couldn't think of any examples that differentiated the two, so I looked it up. According to Swan, they are interchangeable for making suggestions, but 'What about' is used for bringing up forgotten points-- which explains why your (4) sounded a little strange to me using 'How about'. ' Well, I see Swan's point, but to be honest, the difference seems minimal to me.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.