Need some help here: Assuming I need to power a toy motor with a 3V battery... 1. Is there any way for me to generate more power to the motor, at the cost of duration? (Run faster but for a while only) 2. Is it possible to "overclock" a battery so that it support a stronger 6v motor (as usual, same performance at cost of duration)
You need a power supply circuit if you want to increase the voltage going to the motor without changing the battery. This will increase the voltage or electromotive force and allow you to pick a more powerful motor, but it will slightly decrease the overall energy available from the battery as some energy will be lost as heat. If you drain the battery twice as fast it will run for less than half as long because even more energy will be wasted as heat inside the battery in addition to heat generated in your power supply circuit.
A boost converter circuit will use capacitors, an inductor and a switching circuit to increase the voltage output although it will draw more current from the battery than it supplies to the motor and a little will be lost as heat. You aren't increasing the power but you're trading less current for more voltage. You can do the same by rewiring a battery made of two cells in parallel to one made of two cells in series. You will have much finer control with a power supply circuit but it's best to connect the cells in a way that gets you closest to your desired voltage before you input it to buck or boost converting power supply circuit.
Here's an electronics tutorial on how to build a circuit to boost a 3V battery comprised of two ~1.5V AA cells in series to the 5V needed for USB charging: https://learn.adafruit.com/minty-boost and you can read how that was designed at https://learn.adafruit.com/minty-boost/process
Depending on how much of the time you want to spend tinkering with electronics in this project, you may want to build such a circuit from the basic components or you might want to simply salvage it from a USB charger that is sufficiently cheap and small.
More specifics about what battery, what motor, and what load the motor will see may help determine how much current is necessary and whether a particular power supply will work for your project. Switching to a bigger motor may require more current as well so more specifics are necessary if you want help assessing what is likely to work or not likely to work.