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:
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