What I learned from this is a great way to prototype/demo and share an idea before building the whole app. The three improvements you suggest - 1) re-sharing in groups 2) read confirmation in groups and 3) saving - aren't the pain points that I have.
Personally, my pain is just p2p sharing with a person sitting in front (or next to me) - I want the app to understand (say, when both users press a button - its like scanning for a nearby bluetooth connection) to add a person on my whatsapp, allow me send stuff (pics), share a contact, or share a meeting invite - stuff like that. WhatsApp would be great to do this. Proximity-based p2p connections should be quite easy, and apps could make it "feel" more automatic/magical.