>>>don't show that someone liked your post/photo/video/etc.

Right now users get notification only when somebody likes your status. Likes for posts/photos/videos are not part of the "real time notifications" feature.

Sorry, but why?

Helike, updated notifications system was based on the original one which just did not include likes.  You can suggest this improvement to UserVoice

Leveraging already created this post, is 'share' function on the list of next updates?

"Share" with friends in oxwall or with external sites like fb?

Helike, new items for the next build were not discussed yet. So I am not sure which features ( in addition to the ones that are already marked as "planned" at UserVoice) will be included yet.