1) You will need a decent router or the port forwarding or UPnP will screw up when both consoles try to go on live. This will generally cause one or both consoles to drop out all the time.
2) You can play over system link (lan) or via live from the same router. We normally just use live as this allows other friends and players to join as well. I do not see any performance advantage using local lan or system link.
3) Downloaded content can be played on two consoles with 1 purchase utilizing Microsoft's license transfer. The only problem is you can only do this once every 6 months. This can get confusing but when you purchase a game online you effective get two licenses. One is attached to the console and the other to the profile that purchased it. If you use the license transfer to transfer the machine licenses to the other machine then you will have a valid license in two locations providing the profile that purchased the content uses the machine without the license. I do this all the time with my son. He uses his console in his room and I have mine downstairs. Every 6 months we transfer his downloaded content onto my Xbox and mine onto his.
We find having our profiles on pen drives works well. That way we can easily switch between consoles and play split screen on his machine upstairs if Mum wants the TV or he can play his downstairs if he wants the bigger telly or to play kinect. It gives you lot's of options. You could also use cloud storage for your profile but for some reason I prefer the pen drives.