The maximum voltage is defined by the insulation on the wire, not the gauge of the wire. It is the voltage (worst case) that the insulation can break down. The maximum voltage, as well as the maximum temperature, should be printed on the cable.
The maximum current is defined by the cross-sectional area of the cable (AWG number).
The table I usually use is the one from PowerStream: http://www.powerstream.com/Wire_Size.htm
That table gives different current ratings for power cabling (long runs) and for "chassis" wiring (short wires between components or boards in a system). It also details the resistance of the wire, which is very very useful.
There are no exact precise values, only ballpark "rule of thumb" values. The actual value for your specific wire would only be within a range since it'll never be an exact area all the way along. The current rating is also dependent on the ambient temperature, and to some extent the type of insulation (some can handle the wires getting hotter than others). Often a more important factor is the resistance of the wire which, on longer runs and at higher currents, can cause unacceptable voltage drops.
The current, passing through the resistance of the wire, causes heating (\$P=I^2R\$) of the wire itself, and too much current will cause the wire to melt and "fuse". This may go hand in hand with the insulation melting, but not always.
There is no "wattage" for a cable, only limits of the voltage and current. I guess you could say the maximum wattage is the product of the maximum of the two, but that would be a misnomer, since you could be under the "maximum wattage" of the cable but have too much current, or too much voltage. The wattage of a cable only makes any sense when you are thinking about the amount of power dissipated over a specific length of the cable, which is a function of the current and the resistance. Remember - your "working" voltage isn't the voltage that is across the length of cable - that voltage is the voltage drop caused by the current flowing through the resistance (\$V=R \times I\$).
"Ampacity" is an Americanisationalism and could be construed as a portmanteau of Amp-Capacity. Most normal people use Amperage.
You should get a scope on the lines to see what is going on when the cable is connected. If the drivers are "giving up" as you say there is a very good possibility that they are being fried by under voltage or over voltage spikes due to reflections coming back down the cable. The scope can help to identify if this is happening.
Voltage spikes that go over the driver VCC by much more than 0.3V or lower the the driver GND by -0.3V can cause latchup or permanent damage to the driver. If the driver is experiencing latchup you may be able to turn off all power and let the board sit over night. It may work again after the trapped charge in the chip that kept the stray PNPN junction in the chip biased has a chance to bleed away.
One of the simplest solutions to this problem is to place small value resistors in series with the output pins of the driver. Select the resistor size such that the resistor value plus the output impedance of the driver begins to match the cable characteristic impedance.
You may want to also look at selecting a driver/level translator chip built with a slower process technology to slow down the rise and fall times of the driver outputs. This will go a long way toward helping to reduce the amount of potential +/- overshoot seen in the cable.
Best Answer
There are, in fact, ribbon cable stripping tools. For example, see this catalog.
Here's another one:
Typically the tool will come with multiple "blades", or these blades might be available as options.
My Chinese no-name ribbon cable stripper (approximately $8, local store) came with 3 blades, one for 10 x 2.54mm pitch, one for 16 x 1.27 mm pitch, and one for 8-conductor cable for direct insertion into RJ45 jacks.
For mass production, ribbon cable stripping machines are available, which can place, size, cut, strip and crimp connectors onto ribbon cable without human intervention. Sites like Alibaba.com might be useful to search for them.