On the subject of what traffic is being tunneled, I cana answer with the following: If you connect your Android Phone, Tablet, or otherwise Android Powered Device to a VPN (either through settings or a 3rd party app) all traffic should be sent through the VPN (as long as the apps are complaint with the Android System API, apps utilizing 'root' access generally are not and VPN compliance may vary).
On the subject of anonymity however: It depends on your provider and your definition of anonymity. If you are simply pirating movies then your standard VPN should be fine however if your per-say hacking a large cooperation or leaking government documents then a VPN isn't a good idea and you would need something stronger like Tor.
Rooting your phone can have multiple effects and depends on how you manage it. First rooting your phone essentially runs an exploit to grant you more permissions on your phone than you previously had and while it can be a fun project and give you extra features you give up the previous security and YOU ALONE are responsible for the security of the 'su' binary. Rooting your phone will allow you to install deeper security features but requires you to have more technical knowledge to avoid these new privileges from being abused by a rouge app.
An idea you expressed would be rooting and then installing the Orbot, Orweb, and Orwall Suite. That would be a great idea for anonymity. The only thing you would need to make sure of is to secure your new privileges.
Good luck with whatever decision you make. But whatever choice you make should route all traffic through the VPN, Proxy, or Tor not just a single app. Otherwise your asking for data leaks.