Tellstick NET is 'cloudbased'.
I've just ordered some RaspberryPI's and I am planning on using one of them to poll data from from the live service (e.g. temperatures).
You can also use th PI to send commands to the service and the live-service then executes them by contacting the Tellstick net hardware.
Works just fine behind nat. The Tellstickdongle is responsible for keeping the connection to the live-server and thus is more or less immune to nat problems... I've have my TellstickNet 'double-nat:ed'...

It shouldn't be necessary to connect the tellstick net directly to the raspberry, it can reside anywhere as long as it has connection to the Internet.
Very convienient. But, the convinience has a price. The fact that it has to have connection to the Internet is a drawback. If the Internet fails you aren't even able to light up the christmas tree without a good old 433.92 Mhz remote...

With Tellstick Duo you dont have that limitation but instead you will need a server in the network to manage the tellstick.
Communicating directly to the tellstickNet is not yet supported. Maybe if you look around in the telldus forums you can find some code, as I understand the telldus company are welcoming anyone in programming a api (or fw maybe?) for direct access to the tellstick net. They have an open approach.
As an interesting startingpoint you can go to
http://api.telldus.com/ where you can find "
information and sample code for develop against Telldus Live!"
The amount of data used in these requests are negligible. And connections in sweden generally use public ip-adresses, even mobile internet. No worries.
Also: Have a look at
Remotestick for Android and
TellEvent for ios
/stepat