Hi gmlfk0428,
Adding to what @anthony_14117 has already stated here.
As @anthony_14117 stated, 26AWG or larger diameter. The type depends on your environment, but in general, shorter lengths will reduce the likelihood of picking up noise in the cable.
Regarding power, it does not matter whether you use a battery or an AC-DC power supply as long as it’s rated for 12V and can source at least 1A (I would recommend at least 1.5A capability). If you use a 12 V battery or a series of lower voltage battery cells, consider the capacity required to be able to source upwards of 1A for the duration you require between recharges or cell replacement.
This depends on how you choose to control the actuator. If you simply want to manually extend and contract the arm with a switch, then a double-pole double throw (DPDT) Momentary-Off-Momentary (Mom-Off-Mom) toggle or rocker switch capable of handling at least 1A should work (see @anthony_14117’s links above). This TechForum post describes how to connect it so it can control forward and reverse motion.
However, if you are looking for more automated control which takes advantage of the potentiometer positional feedback information offered by the P16 actuator, then you will need an external motor driver board and possibly an external controller. According to the P16 datasheet, Actuonix Motion Devices offers a Linear Action Control Board, the 2495-LAC-ND, which can read the feedback output of the actuator’s potentiometer and use this to control the arm position as desired.
The LAC has multiple control input options, including 0-3.3V, standard RC Servo control interface, 4-20mA protocol control interface, PWM control, or computer software control via the USB connector. In addition to reading the datasheet for the P16, you should also read the datasheet for the LAC to fully understand how it can be used.
I would recommend a fuse to protect your system. The specific one would depend greatly on your overall system design, but a slow-blow type rated for between 1A and 2A is probably the right area to start looking.
Regarding a motor driver, if using just a DPDT switch as described above, then no motor driver should be required. If you want more automated control, then a motor driver, such as the LAC would be a good choice.
A standard diode would not be effective for a bi-directional control switch or if you use the LAC, which has protections built-in. However, in either case, one can provide additional protection by connecting a bi-directional TVS in parallel with the motor. This will minimize back-EMF voltage spikes from possibly damaging external components. A TVS with a stand-off voltage rating from 15V ~ 18V would probably be appropriate.