1- By bridging the ISP supplied gateway/modem, you're eliminating "double NAT". By default they are a little combo modem/router...running NAT. If you put another broadband router behind it, you end up double NATing, and possible having IP range conflicts (if your own router is in the same IP range as the ISP supplied modem/router). Double NAT'ing usually works OK for most internet based stuff, but some apps/games don't like it much, you can get a little performance drop too.
2- Your own broadband modem may have more features and be of higher performance than the ISP supplied one can provide.
The internet light on the combo modem/router is just an indicator that the built in PPPoE login is running. If your own router is doing the PPPoE...the light will be out, no worries.