Go to system preferences, keyboard, and uncheck the automatic adjustment. Then turn it off by pressing the F5 key until the keyboard brightness goes to zero. It shouldn't come on again, unless you manually switch it back on.
Concerning the battery life, just keep coconut battery running and check how much battery power you are using on average. The 13'' MBP has a battery with a capacity of 63.5 Watt hours. This means, with an average use of
10 W you get 6:20 hours battery life
15 W you get ~4 hours battery life
With my 15'' MBP I can stay in the 10 W region with very light web browsing (no videos etc.), but usually I'm a bit above that (12-13 W on average).
If you are not sure why your power usage is high while browsing, you can check Activity Monitor for processes that are CPU intensive - these are more or less directly responsible for the increased power usage.