Why does dough break when kneading, and how to prevent/ameliorate it? I'm very new to bread-making in general; don't assume I'm necessarily doing anything right.

During my last attempt at making quick (baking-powder-based) flatbread, I was attempting to flatten and knead the dough after having let it rest.  What happened was that rather than bending or spreading as one would expect, the dough kept cracking/breaking into pieces here and there.

I have several questions related to this, feel free to answer any/all of them:

(a) What mistakes might have been made ahead of this point, in the recipe or the technique of preparing the dough, to cause this?

(b) On the other hand, what can be done to prevent it from happening in the future?

(c) Given a hunk of dough with this tendency on the table, what can be done to salvage and/or rectify matters?  This can be in terms of kneading technique, or adding anything to the dough to make it more cohesive.
It sounds like it didn't have enough liquid in it. Assuming we are talking about a normal wheat-flour bread dough, I can't think of anything else that would lead to cracking and breaking. Properly hydrated bread dough should be quite moist and elastic, and the only way you can "break" it is to stretch it hard and fast with a pulling motion.

Fixing this situation is hard. You can try to knead more water into it, but it has a tendency to just slip off the surface. Try spreading it out as thin as possible, spraying or rubbing on a little water, folding and kneading and repeating the process.