You can manage some of the yellow ring notifications by opening the Alexa app on your phone and choosing notifications, selecting "Amazon Shopping" and removing notifications about packages out for delivery or packages that have been delivered.
To remove other light notifications, like the green one, you can turn on "do not disturb mode." This is good at night if you don't want your Echo waking you up with alerts.
To do this, open the Alexa app on your phone, choose Settings, select Device settings, then pick the Echo you're trying to manage. Tap "do not disturb," and turn it on. Alexa won't bother you with notifications while do not disturb is active. You can also schedule times for "do not disturb."
You'll still see orange, purple or red lights if you lose a network connection or have muted your Echo, but you can turn those off by fixing the connection or turning off mute.