Any way to automate triggering of "new" DB backup?

Hi,
There are 2 things we'd like to automate.
We have weekly full backup and daily differentials, we do both by specifying:
BACKUP DATABASES [*] TO DISK

1. The first problem is that if someone created anew DB and didn't notify DBA then this newly created DB will produce an error while trying to do differential backup and Full backup wouldn't happen till scheduled day.
Any automated way to fix this issue other than to monitor this manually?

2.Master Database differential backup is not allowed, any way to specify in the synttax "Backup All DBs But... ?

Many Thanx

S