I don't quite understand the discussion about wireless vs. wired connections on the server (note: I'd generally recommend running the server on a wired, not a wireless connection).
In either case it sounds like your issue is one of access from outside the network, right?
If that's the case, this just sounds like a typical port forwarding issue. Your 10.0.0.1 address is a private class address - one that uses NAT to get to the wider internet. No one outside of your network will ever, ever be able to connect to this address.
If you want external access to this server then you need to configure port forwarding on your router. Port forwarding tells the router to accept specific traffic on a public IP address and forward it to a server on your LAN. It just sounds to me that you haven't configured port forwarding. You'll need to check your router manual for specifics on how to do that.
As for the accounts, there's no such thing as accounts associated with an specific IP address, just with the server. As long as users are pointing to the right server there shouldn't be any issue.