1. Output typically refers to the amount of current, in milliamperes or amperes. A battery's output rating can be derived from a "maximum discharge current" specification or by looking at the discharge charts. In the case of that battery there's no specific rating but the charts go up to "2C", or two times the current portion of the capacity rating (yea, the whole "C" thing is very confusing). Since the rated capacity is 1850mAh the recommended max discharge current is about 3700mA or 3.7A.
2. Yes, for both.
3. No. 2000mAh = 2000 milliampere-hours. It's not a current rating, it's a "capacity" rating that lets you know how long the battery will run. You get it by multiplying the current by the running time. For a 2000mAh battery, it should run at 2000mA for 1 hour...or 1000mA for 2 hours, or 4000mA for 1/2 hour. Batteries are not 100% efficient though so you can't extrapolate the capacity rating out to something like 100,000mA (100A) for 0.02 hours.