You can easily pin a post on a Facebook Group to make it stay on top of the page. You can do so on a computer or mobile device.

To turn on anonymous posting in a Facebook group, you must be an admin in that group. Open the Facebook site and select "Groups" from the sidebar, then choose your group. On your group screen, select ...

You can stop notifications from your Facebook groups if you're bothered by constant notifications on the app or desktop site.