Do you mean in the Groups section of the app? There isn't a "groups" tab in the news feed per-se. You should see your friend groupings (ones you've created as well as the ones Facebook creates for you automatically) when swiping sideways through News Feed, Status Updates, Photos, Links then friend groupings. Do you perhaps have a group titled "groups" that has nobody in it. Or facebook may be sending that down to the app as one of their automatically created items.
On the groups themselves (second point) we'll look into that specifically. It should show photos and videos and if it isn't currently it sounds like there may be a bug there.