Hi David,
To answer your questions:
1). As of DS 1.6, there is the feature of integration with the Fiori Launchpad, although I have not seen a detailed SAP document describing the implementation steps. It appears that the integration is between the Fiori Launchpad and a Design Studio app deployed to the BusinessObjects BI Platform. Therefore, I would expect that once you have implemented this integration and added tiles for your Design Studio apps in the Fiori Launchpad, they should also operate as normal inside the SAP Fiori Client. Also, although SAPUI5 M Mode apps would be preferred for the look and feel, I suspect regular SAPUI5 Design Studio apps should also work with the Fiori Launchpad integration;
2). You cannot import a SAP Design Studio app into Web IDE, regardless of whether it is in SAPUI5 M Mode or not and generate a true Fiori app from it. This is simply technically not possible. Perhaps you could develop a Fiori app shell which acts as an iFrame container that references the Design Studio app URL but there is no need for this given option 1 above;
3). For the most part, there should be no reason why you can't run Design Studio apps in a mobile browser directly from the BI Launchpad. As far as I know the only exception might be the online composition feature.
Regards,
Mustafa.