Yes, you can install Windows 7 on a NC10. But it's resource hungry and you would be well advised to replace the 1Gb ram with a 2Gb module.
All the Windows 7 drivers for the NC10 are on the Samsung website.
However, whether it's worth the hassle and cost is debatable. I have it on my NC10 and whilst it looks good it's not as snappy as XP, even with the extra ram. You will, of course, need a portable usb drive unless you install from a memory stick, but that gets a little complicated.
Your call....
As far as the router is concerned some Netgear routers will not work on Talktalk. Do a Google search on Talktalk connection settings and the second item on the list will tell you all you need to know. I suspect it may be easier to stick with the one they give you.