Here are the answers to your questions:
1: I think you can. I have a USB Modem and was able to host my server. Atleast until the modem doesn't let me host it anymore. But I will say, depends.
2: What local IP? If your meaning localhost:port/127.0.0.1:port, than it will only show to your self. It will never appear in an internet list for anyone. Just add it to your favourites list.
3: Famous question. Here is Storm's Tutorial
. But if your meaning modem instead of router, I once found a side saying that Modem doesn't need any port forwarding.
4: Sorry.. Don't understand. HOPE IT HELPS..