Explain how to change the staus profile in the notification once when I selected the other profile by mistake?

Go through following step and check it :

SPRO-->Plant Maintenance and Customer Service-->Maintenance and Service Processing-->Maintenance and Service Notifications- ->Notification Processing-->User Status for Notifications- ->Define Status Profile-->Assign User Status to Notification Types

How to change the status of the equipment after going outside of company for repairing, so what changes is done in configuration?

For equipment which is going out of company for repair, you can define your own user status in SPRO, through following path :

SAP Customizing Implementation Guide --> Plant Maintenance and Customer Service -->Master Data in Plant Maintenance and Customer Service--
>Basic Settings-->Define User Status.

For e.g. you can maintain user status as Under repair or inactive.

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