Hi Monika,
Q1. What kind of error are you running into? Make sure that you are using the fully qualified domain name in the url when accessing the fiori launchpad. The Webdynpro app will need the FQDN and using Ip address will not work.
Q2. When you upgrade to SP02, the catalog will include more apps, and more apps will also be assigned to the groups from these catalogs. If you didn't see the new apps in the assigned groups, you will have to clear the cache and reset the group.
Q3. I have not done a SP02 upgrade yet, so I have no specific experience that I can share on this. But I would assume that you will have to upgrade the entire stack including the frontend components (gateway) and backend (S4CORE plus other backend components that is needed). You will also have to check for note for the upgrade, and if any app doesn't work, you will have to search for notes to fix each app.
I will update you once I have specific knowledge of this .
Willie