Can a gear motor w encoder be 60 ft away from controller?
Part of your answer is pretty straightforward. The driver can drive the motor at this distance, as long as you make sure to use reasonably thick wire. 20 ga ought to do. 

But. Running the motor will require careful shielding of your cable, since the PWM noise will be radiating like crazy if you don't. Twisted pair for the motor drive at least, and probably shielded twisted pair.

The encoder is a big maybe. A lot depends on what the frequency is of the encoder steps at full speed. Data sheet says a maximum of 7000 shaft rpm with 980 steps per revolution. That's 114 kHz. The encoder data sheet says that these are open-collector drivers. This is not usually great for these distances and frequencies. I think you'll need to buffer the signals using some sort of differential driver, such as an RS485 driver. This would mean that you'd have to provide a small (1 IC plus a regulator)interface board at the encoder end of the cable, which would need a regulator to drop the +12 supplied by the controller board to +5 for the drivers. You'd also need a small (1 IC plus a regulator) receiver board at the controller.  And you'll need to go from 4 wires to 6, with one twisted pair for the power and ground, and a twisted pair for each of the encoder channels.

The driver will drive each motor in either direction independently. Actually, you can select rotation direction for a given command direction simply by reversing the motor leads. Be aware, however, that if you try to reverse direction at any real speed, you'll hit current limit on the driver. You'll need to provide a ramp command to the motors (that is, a gradual change in speed command) in that case.

Also be aware that, with these motor/encoders, you will have a very great deal of trouble trying to maintain a fixed shaft angle. At best, you'll get a small oscillation of +/- 1 encoder step around your desired position. At worst, it will be larger than this, with considerable power being dissipated in the motor. These motor/encoder sets are excellent for maintaining a constant speed of rotation - fixed position, not so much.

If you're thinking of a CNC-type positioning setup, you're better off going with steppers.