1) What is the difference of having
a) Tools -> Options -> Startup -> Run remote server on port: <port> or
b) Starting from Services & Plugins -> Library Server and putting port <port> there?
1) a) Remote Server is what is needed. It runs a web server that provides a simplified remote access user interface. It doesn't share files.
1) b) Library Server shares the actual media library. The client MC downloads a temporary copy of the complete media library on connect. The filenames are translated to streaming addresses and any kind of permanent write access is not possible. This server is not needed for what we are trying to accomplish.
2) I have option 1a running and Oddcast can hear the music ok and I have autoconnect on here, so this is ok.
Oddcast does not connect MC. It grabs the decoded audio signal after MC (from the OS level audio driver). It uses LAME for encoding that signal and streams it to the Shoutcast server. I suppose you mean that.
3) Any user can now connect to my computer by putting my ip and correct port number in browser address field. Can I not password protect this? Or is it supposet to work like this?
As I said earlier the Remote Server does not have a password protection. It should have. It is possible that someone connects to your MC and plays your wife's country music.
4) If everything was ok, should I not be able to connect with Media Player to http://<ip>:<port> by selecting File -> Open URL... ? Other user could not connect and I could not connect with 127.0.0.1:<port>
127.0.0.1 is your PCs internal address. You can use it only on the same PC. You can also try the real IP address locally. I meant that you can use this address for trying the web browser connection to your local MC's Remote Server.
My Remote Server uses the port 9696. I can connect it on the same PC with a web browser address htpp://127.0.0.1:9696 or htpp://192.168.0.15:9696 (this one is the real address of my PC). Only the latter can be used on other PCs on my LAN.
For connecting the Shoutcast server with a player program you need to use a different port (the default is 8000). Try Winamp v.2.95 if other programs cannot connect.
5) I think I'll have to wait until next week when I can bring my work laptop home and test this again having both computers here...
... and we have not yet talked about opening or redirecting ports in the firewall and what to do if your employer allows only the ports 80 and 81 for http connections. BTW what kind of Firewall you use at home?