Regarding the new notifications, I really like them, but if the icons were white/grey when there's no notifications and changed to the green/yellow/red when there's one they would be much more noticeable, I'm afraid as is it could be some time before I notice any new one, though warnings and alerts I also get an email.
As an alternative you could have only one icon and the color would change according to the most serious notification while the number would indicate the total amount, e.g.,
white/grey - no notifications
green - notices only
yellow - at least one of the notifications is a warning
red - at least one of the notifications is an alert
Don't know if it would be an easy change, but you asked for suggestions