Hi Chris
Firstly, Yes, it is better that the Tap slips within the drill chuck, than being broken.
Often a Tap will slip in the chuck, but the thread can be completed by slackening and withdrawing the chuck, and replacing it with a tap Wrench. You can then continue tapping, being able to feel the load on the tap. With larger sizes, say 8mm / 5/16" upwards this can be great enough to cause a Tap to slip, without there being a problem.
This is at least "fail safe"
Obviously, when using a Tap Wrench by hand, it is important not to cause any side (Bending ) load on the Tap – That way lies disaster to both the Tap and the workpiece!
With regard to gears, DP means Diametral Pitch, which is the ratio between the size of the gear, and the number of teeth. A 20 DP gear with 20 teeth will have a diameter of 1.1" The formula is: OD = (N+2 ) / DP
Module gears, being Metric, are the same, but using mm instead of Inches, as the unit of measurement.
The Pressure Angle affects the exact shape of the tooth, so meshing 14.5 and 20 degree gears is a very bad idea, which will, at least, wear both gears, even if the DP is the same
Myford gears are 14.5 degree P A, where nearly all modern gears are 20.
Ivan Law's book, "Gears and Gear Cutting", No 17 in the Workshop Practice Series, will explain a lot more about gears ever than I can.
HTH
Howard