Can I notify customers when a request is updated with a particular status?
Yes, you can notify customers when requests are updated with a particular Status. To achieve this, you can setup Workflow Rules and Alerts.
Goto Setup > Workflow Settings > Workflow rule > Create new rule for Request module.
Then create alert, Goto Setup > Workflow Settings > Workflow Alert > select E-mail Template > select the Support Agents that you would like to notify (this is optional) and check Notify Contact.
When a condition is met in workflow rule, the alert is automatically triggered.
For more, refer Workflow Rule.