All minions do physical damage, because they're presumably manning some sort of defences, throwing rocks, etc. Trap damage types are relatively clear, but I'll update their descriptions anyway.
They are not really clear. For example, my knight had "careful: looks for traps first" character and fireproof, coldproof, spike trap evasion abilities.
Does fireproof and coldproof mean that magical traps are ineffective against him at all, or do they deal reduced damage, or maybe they deal normal damage and theese abilities just boost resistances during battle?
Does "spike trap evasion" mean that spike traps are ineffective at all or do they deal reduced damage?
What does "looks for traps first" mean?
Do theese abilities affect only knight, or his whole party?
There is very little in-game information.