1.)After using them I found out that they do not go into a sleep mode. They stay on all the time as long as they are connected to your phone. If it has no connection to a phone, I found they turn off by themselves. So to answer your question, yes I would turn them off when your not using them to conserve battery life.
2.)If you turn the Bluetooth off on your phone and turn it back on I found they normally connect automatically. But you can always go into your phones Bluetooth settings and just click on the Jaybird Headphones and they will reconnect. No need to pair them again. Once they are paired they will stay paired.
Hope this helps.