I window shopped for a small size battery. On the battery specifications, there are:
What does Pulse Current mean? Does it means this battery can supply 190mA at a time? If there is no resistance between the terminals, can this battery supply power for 190/85 hour?
What is Cycle Life?
Do I have to connect a resistor when I operate the micro motor with 5v 500mA power source? [sic]
First, read a bit on meaning of word pulse.
The pulse current is the maximum current that battery can provide. If the current goes higher, battery can be damaged and will probably start overheating. The missing part is definition of the pulse. Somewhere in the datasheet it should be mentioned how long the pulse lasts. The other part which is also important is continuous current. It is the maximum sustained current which battery can provide and is usually much lower.
Cycle life I believe means the number of times the battery can be recharged.
One part you also missed are definitions of power, current and amount of electric charge. The charge a battery can store is measured in coulombs. It is shown in mAh because of the relation between those units. \$ampere=\frac{coulomb}{second}\$, so when you multiply ampere by second, you get the charge. the milli part is because traditionally small batteries have too low capacity to warrant use of Ah (which is used for lead-acid batteries). So to calculate roughly how long the battery will last, you need to divide the total capacity by the current you will draw from the battery. So if you're planning to use 190 mA, you'll get around \$\frac{85mAh}{190mA}\approx 0.44h\$. Do note that the battery will most likely not survive such use, because pulse current is usually higher than continuous current, which you'll need to take into account if you want to use battery with electrical motor.
As for resistor part, well the best idea would be to control the motor using variable voltage to set the current. So yes, you can use a resistor to limit current going through the motor. Do note that the resistor will use some of the power provided by the battery.
