you can change the update preference to update during later times, the update settings are different for each carrier so you'll have to call and check with your provider.
Additionally, the phones have setting to reboot during the night so that the phone doesn't get a lot of cluttering data. You should be able to disable in the settings. The notification setting is likely due to safety/security protocol, you'll have to remove locks.
I haven't tried so I'm not completely sure, but try using a routine to disable locks based on time or location, see if this help prevent phone locking and preventing notification from not alerting.