You need the router if you want each of the clients to be able to share the same internet connection. Alternatively, you can use a proxy server and accomplish the same thing. There are situations where it might be preferable to use one of each.
Redundancy is a good policy in all areas of communications.
Microsoft GUI's are a good illustration of that principle. I know about NAT, I don't personally have any expertise in that area. There are numerous forum members who do. Net is the opinions of its users. Such opinions may not be accurate and they are to be used at your own risk.