By default your account is set to automatically watch threads you post in etc. You can turn that off by:
1. Clicking on your profile name at the top right.
2. Choosing Account details.
3. Clicking on Preferences under Settings sections.
4. You can turn off the first four at the content options.
I don't think messages from MH staff can be silenced
If you're talking about your browser giving you alerts, then:
1. Click on the lock icon on the address bar
2. Choose block from the popup under the notifications secion.