1. The only way to get more features is if you either sign up for the organizational account or if you have a GIS server. What I did to circumvent the 1000 feature limit is divide my list up in smaller chunks.
2. I think you are only able to query hosted feature services, not the once you can upload for free.
3. With an update, they have released earlier this years, they have changed how groups work. You are no longer able to share maps with just group members, if you have the free account. You can only make the maps private or public to all. You need an organizational account to be able to share maps just with groups.
4. I think the only way to do this is opening your maps in a browser. Again if you have an organizational account you are able to open maps in the ArcGIS app.
I hope this helps!
Tim