Okay, I think I got what they meant by "defeated by another card" . If you draw 2 enemies, one uses Craft and another uses Strength,if you kill one and are defeated by the other, you still move back.
There are other possible cases: when you draw Two or more Enemies, you kill one Enemy (e.g. with a Spell) and get defeated by the remaining. They could be all Strength Enemies in this case.
It's worth noticing that "defeated" means "lost a battle or psychic combat, after comparing attack scores". It doesn't mean to lose a Life in combat, so Armour will not prevent your Character from stepping back one space if he loses a combat on a Stairway.
As for question 1, I suggest you thoroughly read the Dragon tower section in the Rulebook (pg.13) because I suspect you missed something. You always advance 1 space after a turn in the Dragon Tower (you don't move at the beginning of turn as normal!), plus 1 additional space for each defeated Enemy. Only if you lose a combat on a Stairway, you move back 1 space (no matter if you killed other Enemies).
I consider that the "Turning Back" section is also applicable to the Dragon Tower. If you started ascending and want to move back to the Plain of Peril, you follow the Turning Back procedures (pg.13).