Facebook group members without profile link

When you are creating the event, there is an option that says "Invite members of the host group to this event", but I'm not sure that it is possible to do so after the event has been created -- the option is no longer there when you go to edit the event or invite friends. I think you will have to invite the group members right from the start when creating the event, or else select them manually afterward.

If you post a video to a group then all members of the group will be able to see the video. If the group is open then anyone who views the group will be able to see the video.

From the Facebook FAQ

How do I post videos to a group?

Group admins can select whether videos can be posted to a group from the Customize tab of the Edit Group page. If videos are enabled, the admins have the choice to allow either all group members or only other admins to post videos.

If you are allowed to add videos, you can do this by clicking the "Video" icon in the Publisher at the top of the group’s main page. If this is an open group, the videos will be visible to everyone who views the group. The videos posted on closed and secret groups are only visible to other members. Admins always have the ability to remove videos that they do not want to be associated with their group