First question; Honor = starting morale. The higher the less likely troops are to root.
Morale is modified by some events, such as, losing, being charged by cav, being flanked, general dies, other troops rout etc.. (see sticky 'new please read this first' topic)
Disciplined makes units resistant to some of those modifiers such as general death and non disciplined or non elite troops routing.

Second; look at what is available in the dungeon. IMO, it's a normal feature of the game, and to get kicked from time to time is part of the fun.

Welcome,

Louis,