How do I find the voltage range for an unknown DC motor?
A simple model for a DC motor is \$V= R*i + e\$, where \$V\$ is the terminal voltage, \$R\$ is the motor resistance, and \$e\$ is the back-emf voltage.  

R can be measured as I said above in a comment and which I'll repeat here.  Resistance can vary on a DC motor due to brush contact. The best way to measure resistance is to take several measurements and average. If possible, lock the rotor and then apply a small current to the terminals. Measure voltage and current and calculate R = V/I. Typically you this test would be done at ~25% rated current. Repeat several times and average. There is a dynamic test, too, that can give even better results - do the same as I just said, but instead of locking the rotor, back drive the motor. 50 RPM would be sufficient speed at which to back drive the rotor.

\$e\$ can be determined from \$e = K_b* \omega\$, where \$K_b\$ is the back-emf constant (units of V/(rad/sec) or V/RPM) and \$\omega\$ is the speed in the same units as \$K_b\$.

You've already found \$K_b\$.  It is just \$\frac{16 V}{570 RPM} = 28.07 \frac{V}{kRPM} = 0.268 \frac{V}{rad/sec}\$.  As somebody else mentioned, the torque constant of a motor is equivalent to the back-emf constant, so \$K_t = 0.268 \frac{Nm}{A}\$.

At locked rotor, you know that \$V = R*i\$ because \$e=0\$.  If you solve for \$i = \frac{V}{R}\$, you can find the current when the rotor is locked at different voltages.  And from that current, \$i\$, you can solve for the locked rotor torque at different voltages:  \$T_{lr} = K_t*i = K_t*\frac{V}{R}\$.

You can also determine the maximum speed of the motor at different voltages using \$V= R*i + e\$.  If you assume \$i=0\$ when there is no load, that equation becomes \$V=e\$, which becomes \$V= K_b* \omega\$, which becomes \$\omega = \frac{V}{K_b}\$.  

Once you have the stall torque at different voltages and the maximum speed at different voltages, you can plot them on a graph with speed on one axis and torque on the other axis.  Connect the lines and you have various speed-torque curves at different voltages.

There are a lot of assumptions in what I wrote above.  The 2 main assumptions you should be aware of are  1) that the motor stays relatively cool (so the resistance doesn't change) and  2) that the no-load current is zero (in reality it won't be).