OK lets get one thing straight. Linux isn't Windows, it never has been. Unless you want to buy Crossover Office (check it supports the apps you want) then most likely it won't run on linux. This isn't a problem with linux, its just that most developers program for Windows. Its also the same with drivers. Don't expect to put your drivers disk in and install your device for linux. Linux is totally different. It may take some tweaking, but Mandriva has excellent hardware detection. You should be able to automatically use your wireless adapter without having to install additional drivers.
You're question for the router/windows/linux combo isn't too clear. You would connect to the wireless network and have internet access. The data doesn't route through the windows PC if you use a router, instead it should go directly to the Linux computer.
Limewire uses the Gnutella network I believe, there should be a linux client which can also connect to the Gnutella network.
I'm pretty sure MSN won't run on linux, unless it is specifically supported by an emulation program. Instead, I use the free GAIM client. It can connect to a wide variety of IM networks including MSN. You might have to fiddle around with its settings to get most of the functionality of basic messenger. At the moment I have gaim to notify me with mails from hotmail with Firefox as my default browser.
Dreamweaver is supported by Crossover Office, but you will have to buy it. However Crossover won't support the other Adobe applications, only Photoshop is apparantly supported.
Empire Earth can be run with Cedega, which is worth the small fee. Cedega will run a wide range of games, so you'll be able to play different games without any hassle.
At the moment, some programs in Windows aren't yet available for linux, so I have a dual boot. To dual boot, you simply install linux on top of Windows (use a partition manager to create an empty partition or leave it as not partitioned to install Linux on), and every time you boot your computer you'll get a menu to choose which OS to load. Therefore if I do need to use windows, I can do.
As I said before, Linux is an entirely different OS, based on the framework of Unix. So drivers and devices are handled differently to Windows. Whats happened is that Windows is so widely used that it has become the default paradigm for an OS to some.