ttran Either way here is the answer to both:
Can notifications be turned off to user in inbox?
Not at the moment but it is being looked into for a future release in the following manner, Global off switch, probably. Turning off per-user will be a Pro feature.
To disable notifications in the shout:
ACP Settings/DragonByte Tech: Advanced User Tagging - General Options
Their is options there for:
Shoutbox Integration
Advanced User Tagging can add an additional tab to DragonByte Tech: vBShout with alerts for Tags and Mentions.
If you don't use vBShout, you can ignore this setting.
If you don't want to use this feature, uncheck all boxes.