Put the same Google account (not gmail account) in the S6 that you have in the S4. (Make sure the S4 is set to sync apps.) The S6 will sync all the apps from the S4 (actually from the cloud, where the S4 apps were stored).
You can also install smart switch from the play store on both phones. It won't bring every app (I have seen a few that did not come over), but a very large majority, as well as pictures and videos.
Not necessarily. Pictures could be accessed with a computer IF you had no pin/password /pattern screen lock, just swipe to unlock. They may have been synced to your Google account, the sync photos option is left on in Accounts - Google, how many depends on how often you turn master sync on.
They would also save to Google+ if you have a social profile there.
Google / Gmail would have your Google Contacts, Samsung would have your Samsung contacts, Device Contacts would only sync with Kies on a pc.
If you cannot remember how to log in to Google on a pc you can get help there.