You can work with the application immediately as it connects to ArcGIS Online, where you can search and browse for maps. You can view these maps and edit data on the maps (if this is enabled). To view your own custom maps, first you will have to create your map in ArcGIS Online. You can then keep this map private to you or share this amongst your groups or make it public. In the ArcGIS for Android application you can login to see your personal maps.
Yes, although the application has not yet been optimized for the tablet.
To be able to click the map and view details of features on the map you will need to have authored pop-up windows for your layers. For details, see Configuring pop-up windows.
If you do a long press on the map (tap and hold for a second or two) you will be presented with a magnifying glass. This shows a magnified picture of the map wit a cross hair and allows you to move your finger over the feature more accurately.
Secure map services using token and basic/digest http security are now fully supported.
You will need to publish your maps to an ArcGIS Server service before you consume them on your Android device. Once you have your services published you have two options, you can either make them accessible to the internet and then author an ArcGIS Online map or you can add a map to your Mobile Content Server (which comes with ArcGIS Server). You can access ArcGIS Online and Mobile Content Servers from the ArcGIS for Android application.
For more information on ArcGIS Server Mobile Content Server, see maps.pdf.
You can also upload shapefiles to ArcGIS Online maps, this data will be visible in the ArcGIS Android application, but you will not be able to edit your data or update your data directly in your geodatabase.