Can anyone create a system alert?

And will only the person who created the alert be able to delete that system alert?

Anyone can create a system alert but alerts won't be sent unless they have the "Shared Alerts" permission. 

At present, only the person who created the alert can delete all alerts. 

The Support Team can also assist with delete the alerts from the backend. 

References:

Shared Alerts

To enable shared alerts for a particular user:

1. Open Control Center > Manage Users  
2. Locate the user who has requested the ability to share alerts 
3. Scroll over to the Shared Alerts setting and toggle it on