Hi ,
For question #1, you are correct. You will need an ArcGIS Online for Organizations subscription to publish the shapefile as a hosted service, which you can then add to a webmap. If you have a subscription, the option to publish a hosted service from the shapefile will be present (and enabled by default) when you add the .zip file.
For question #2, the shapefile is just stored with the saved webmap. A hosted service will not be created if you add a shapefile this way.
Hope this helps.