Can I do this by making the new group "Owner" for all videos?
Yes. If you make the new group an owner or viewer of the video and the display check box is checked then it show up in the new group. We don't have a bulk way to do this for all videos, you'd have to do it one by one. (Please add your votes/comments to this idea in our ideas forum for bulk operations: https://techcommunity.microsoft.com/t5/Microsoft-Stream-Ideas/Bulk-Actions-Add-multiple-videos-to-ch...)
If a video has Group A, Group B and User C set as the "Owner", what happens when someone deletes Group A? Will this retain the video with Group B and User C?
Yes it will. In Stream the video is the main source of truth and it references/is permissioned into other groups. So when you delete a group it doesn't delete all the videos permissioned to it.