To fix points 1 & 2, they could overlay the label to the left and have the caret start to the right of the label, like in MailChimp's login page: https://login.mailchimp.com
Oh, that mailchimp page is nicely done. Very simple implementation too: they basically just gave the input element a bunch of left padding and absolutely positioned both it and the label element inside a wrapper div with position:relative.