1.Can you connect at all? If you are connected to ADSL your router does not need to'dial' - your connection will be a PPPoA connection and your router can be set up to assign all the settings directly from your ISP (IP addresses etc)-all you need to give the router is your ISP username & password or whatever they need for you to log on - theres no phone number to put in.
2. The PC on which the document is created is your fax server - you need software capable of converting documents for transmission by fax - MS Word can do this and you either then use fax software or an internet fax service.
3. Assuming all your PC's are using the same OS I don't know any obvious reason why one wont copy the files. Could be several reasons.
4. Internet Explorer,Netscape & Firefox browsers are capable of all that - depends if you want whole network control from one PC, or are happy to log onto each one and check each browser to see where its been.
5. Depends what you mean by sharing - you have one connection and one contract - you can connect as many PC's as you like to your network subject to the download limit in your contract - obviously if you intend to use 3 PC's a lot on a small download limit you will be using it 3 times as fast!