NetLimiter can monitor and control the bandwidth for individual programs. This way, you could keep an eye on rogue/unknown programs that connect to the internet and also on how much traffic is generated by regular stuff like surfing.

Browsing can take up a lot of bandwidth. Especially with flash adverts, AJAX, youtube and stuff.. If you have a low data cap, I suggest using the Opera Browser (with Turbo mode enabled, so traffic is compressed) along with an ad filter. (like Ad Muncher. Not free, but it's the *best* there is.)

When your computer is off, the LAN light might stay on because most PCs support what is called as 'Wake-on-Lan', so that a computer can be automatically turned on upon sending the right signal. On the other hand, sometimes a router might show the LAN light on even if it the cable isn't connected. It's just a harmless bug, rebooting the router should fix it.

Finally, yes, you can be a non-admin, but not having a username and password? I can understand not having a password, but Windows is a multi-user environment and you need to have *some* sort of username. What I suggest is creating an account with a password, but have it auto-login so that it won't prompt you for a username/password.