These questions reveal that you've never read any details about the design of the network.
Please go read this article:
The SAFE Network from First Principles: http://www.youtube.com/playlist?list=PLiYqQVdgdw_sSDkdIZzDRQR9xZlsukIxD
And watch this:
To answer directly your questions:
1) Yes, you can store files, stream and "serve" static and dynamic websites. You can build chat apps, email, videoconference, browsing, "hosting", etc...
The ones challenging are gonna be real time gaming or any other app that requires very low latency.
Watch some old sample apps here:
2) VPN connections are easily detectable, easily banned, and if you are using the wrong protocol (such as PPTP), also easily crackable (on the fly). Also, it doesn't guarantee anonymity, if the VPN gets a subpoena you are done.
3) Targeted Ads are the cancer of the internet. The monetization model is different in the SafeNetwork: read about how SafeCoin works. You can make money without selling your soul.
4) What type of hacks wouldn't be possible on the SafeNetwork? How about all of them?
As I said, there are no servers. ALL remote exploits for servers are obsolete. No Apache, no IIS, no nginx, no FTP, no mySQL, no MSSQL, etc...
DDoS isn't possible as well.
5) And this should be obvious at this stage: your data basically doesn't exist anywhere until the moment you make sense of it reconstituting it with your credentials.
Sony leaks and Target hacks are impossible in the SafeNetwork.
You could still tailor attacks targeting specific individuals, but centralized database dumps would be impossible because there isn't one. (Although if hardware tokens are implemented for authentication, it would practically become impossible to hack remotely even in tailored attacks.)