The core SSM screens are not optimized for iPhones now, but adding the ability to do things like view and approve Entry and Approval data via the iPhone is definitely on our radar.
Yes, your iPad must be connected to your corporate network to access SSM data IF SSM is deployed within the org's firewall. If SSM is deployed in a hosted environment (e.g. via a partner hosted or HANA Enterprise Cloud environment) then connection to the corporate network may not be required.
Yes, at some point we will have a publicly available, self contained demo that highlights the SSM iPad optimized screens. At a minimum we'll have a recorded demo available on YouTube soon, similar to the CI demos up there now...see the links below.
CitizenInsight Overview - CitizenInsight iPad App Overview - YouTube
CitizenInsight Administration - CitizenInsight iPad App Administration - YouTube