My laptop's 1-year warranty includes battery and the battery does not last long anymore. Does this mean that I can get a new battery with the warranty?
It probably depends how long is long. If your battery is nuked after 15-30 minutes it might be replaceable, if its like 2 hours when you used to get 3 good luck.
Mine lasts about 2 and a half but I usually have my screen brightness up all the way.
My laptop's 1-year warranty includes battery and the battery does not last long anymore. Does this mean that I can get a new battery with the warranty?
System Profiler > Power > Current & Original Capacity and Cycles.
If you have less than 300 cycles, and the current capacity is less than 80% of the original, you might be able to replace it.
Hard to say. OP is still within their first year so there should be no reason the battery should be acting up. In your case, even though it is under 300 cycles and capacity is less than 80%, your Mac is about 3 years so battery life could be degrading based on time and how you conditioned your battery over the years. If you want, check it out at the Apple Store but don't expect anything to happen.