Part of the reason it may be snapping is as DKM stated that it may need to rest. If it is breaking and dry as you stated I suspect that there is too much flour incorporated into the dough. This can create a better cracker crust, but too much will cause the dough to become brickish in nature. It won't be very workable and will not result in the crunchy , yet chewy texture you might be hoping for.
Mixing dough profesionally, we did not use an exact ratio of water to flour. Now mind you we were using 25 lb bags of high gluten flour at a shot and mass producing dough for the nights pizzas, but the principle is still the same on a smaller level. When the mixer is kneading the dough you can tell you are getting close when it starts to hold its shape, while not "sticking "to the sides of the bowl. It should be slightly tacky, but not sticky when you touch it. It should still be pliable, yet again, not sticky.
The best way I know of to accomplish that is to incorporate the flour in stages. You want to add the majority of it till it starts to gather and then let it work while adding low amounts, and letting it work in, before giving it more flour. This is not true for all crusts, and I am sure there are some with more knowledge on the matter.
The overnight run in the fridge, as stated before is a way to slow the rising process. This allows for the gases to work the chemical change in the glutens and ferment the dough more than it would in a few hours on the counter. You could in thery let it sit on the counter all night, but the process would be way to fast and you would end up with dead dough. Counter top works, but you generally get a much better texture & flavor by putting the dough in the fridge overnight. You also eliminate the "bready" texture somewhat more.
I generally do not use eggs in the dough I make as it gives the crust more lift. They basically strengthen the bread and help it keep shape, or so I have read.