Is there a way to remotely access my desktop and transfer files over the net to my S3?
To transfer files you can try AirDroid. But it is free only when the device are on the same wifi network. Access via mobile data is limited to 100 MB/Month.

For video streaming, you can try Emit. The free version puts ads on your stream and you can stream to your phone even when not on the same network, but you'll need to mess a bit with ports.