Will I loose iPad application data when I switch Apple ID?
I believe this depends on they way the App is set up. If an app backs up its data on iCloud then it will not be able to retrieve it as each Apple ID has separate iCloud storage space. On the other hand if the app uses its own server for syncing (and you use the same login details) I would imagine it will restore data appropriately. 
However purchases made with one Apple ID are not available to another Apple ID. I am not sure if Apple offer transferring purchases but I guess you could contact them to see it they could do so for you.

1) I don't think changing Apple ID will cause any data loss. I switch between two and never had any issues (I would however check with Apple)
2) Yes, but you might have to download them first if not already on the iPad.
3) This could happen as the apps will have to be updated and since iOS5 most apps have heavily changed both visually and the way they work with say iCloud.
4) As stated in (1) I don't believe you should loose any data but you can only have one Apple ID active at a time.

Make sure you take a full backup on your computer before making any big updates like moving to iOS7 from iOS5.