It's not unusual to find that under near-full-power-out conditions the motor will be about 50% efficient. This is a big motor but it still applies: -
Next, you estimate how much mechanical power you need (2 pi n T) where n is revs per second and T is torque in newton.metres. If your dc motor's data sheet doesn't provide this information (like the graph above) then get one that does.
If you don't know how to calculate your mechanical power requirements you need to learn and start with: -
Force = mass x acceleration courtesy of Isaac Newton
Mass is what you want to move and acceleration is final speed divided by time to get to that final speed (i.e. what you want it to do).
Force x distance = work done and work done per second = power.
Don't forget friction as a loss and if it moves fast then there will be other losses due to moving air around.
Well, first we need to clear-up the differences between the two power-supplies. What you are implying is that the "regulated power supply" is current-limited and that the "Unregulated power supply" is not current limited. "Current-limited" is different from "regulated", which typically refers to the output voltage.
Also, I will be discussing a brushed DC motor, as no other type of motor really applies to your questions.
Having said that, most of what you list is true. I will refer to each point as 1 through 8:
1) True.
2) Not necessarily true. The Motor only pulls the current necessary to provide the needed torque (torque is directly proportional to current). If there is not much load on the motor, the motor will speed-up until the back-EMF and motor resistance balances the power-supply and limits the current at equilibrium. If you increase the load, it decreases the speed, which reduces the BEMF, which allows more current to flow, which increases the torque. So it is the load on the motor that will determine if you exceed the power supply's maximum current.
3) Also not necessarily true. Again, the current that the motor draws is determined by torque, and increased voltage may or may not cause an over-current. If the current is controlled, as it is with a motor-amplifier, it is customary to have a power-supply that exceeds the motor's voltage specification. I typically drive 24 volt motors with anything from 24 volts to 160 volts.
4) Mostly true, but it depends on the performance that is required. Reducing the voltage reduces the speed, since the voltage is required to counter the BEMF as the speed increases. A lower voltage does not lower the torque, which is solely determined by the current.
The current limited supply does not make much difference:
5) Again, true.
6) Well, no. The supply is current limited, so nothing bad happens. You simply cannot get your rated torque out of the motor.
7) True. It also limits the torque.
8) Mostly true (and mostly true for 4, as well). The only thing to keep in mind it that it is the motor's torque requirements that is limiting the current, not the power supply (unless the motor tries to exceed the supply's current limit).
Hope that helps
Best Answer
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.