What is the max resolution / time? 1 millisecond?

I want to send out pulsed signals (on / off) from a pin at about 2,000 Hz. I want to vary the speed and the pulse width (power). PWM is obvious but what is the fastest time interval? I think the UNO is 1 millisecond, or 1/1,000th of a second. What about the DUO? Are there any other boards that can do this through something like LabView?
Thanks a bunch.

I think the UNO is 1 millisecond, or 1/1,000th of a second.

No it is not, it can be way faster. I have used it at 125KHz and it will go faster. It is all about the pre scaling on the timer's clock.
The Due will be even faster if you push it but there is no need as a UNO will do what you want.

OK Awesome. I researched the prescaler and it looks like that is the right direction. Now I can increase all the timings to the right range for the motor sequence. Now here is the second part of my problem. I want to send the on / off signal to multiple pins at that frequency with exact delay sequence to coincide with this frequency. Does the prescaler increase all the timings on the board so the delay between pins will match the output frequency in phases?
I know you are thinking that I am trying to drive a 3 phase motor but it is actual a bit different. I am building a custom multi phase ring motor but each series of EM poles on the stator has it's own independent loop. No star or delta pattern. So I am basically trying to build a custom ESC for a custom motor. I can easily connect each pin out to a relay to increase the power to the motor. And I can add a variable resistor between the motor battery and the individual relays to adjust power level. Then I can write the same variable to the resistor and the frequency scaler to adjust speed and power levels simultaneously. Essential I want a Volt/Frequency controller so I can gradually increase the voltage and frequency at the same time and also have a number of outputs pulsing in series. I know it sounds complicated but I don't think it is. I have seen lots of people try this online for a standard 3 phase motor but I think their problem is they are trying to work with the multi phase motor loops which require one of the three lines to be a feedback path which is also a supply path for the next phase. I think this unnecessarily complicates the whole process which is why most of the solutions I have seen get very complicated. Change the motor design to independent loops and I think it would be much easier. I can install a seperate sensor into the motor to read the position if a want but I don't even think that is necessary the way I designed the motor poles. An Ohm meter on the ground might be more effective to adjust voltage based on load feedback and keep the speed/frequency.

An Ohm meter on the ground might be more effective to adjust voltage based on load feedback and keep the speed/frequency.

not sure what you are saying here.
You can't use an ohm meter in a powered circuit. It works by putting out a voltage and measuring the current coming back. Any currents in the circuit from other sources are going to mess up your reading.