The 1 point of damage is assigned as any other trap damage (i.e., it can be prevented by thieves or the paladin). The 2 additional damage is a special effect of the trap. Because of this, it can’t be prevented by anti-trap abilities (neither by thieves nor by the paladin) even if the first damage was prevented.
(The text on the card explains that thieves cannot prevent the damage, but this applies to paladins as well. The card will be corrected in later editions.)
Note that the additional damage is assigned at the end of the round, even after the Conquering Step. That means that even if this damage eliminates the last adventurer, the party can conquer a tile before it happens. Also note that if the adventurer you hit is eliminated by monsters or by fatigue, these two damage are not dealt. (They do not transfer to the next adventurer.)
The damage is dealt even if there was no Conquering this round.
(The “At the end of the round (after Conquering)…” text on the card just specifies the timing of these events.)
You can imagine it this way: prepare damage blocks above each adventurer according to the trap text, as if there were no thief or paladin (but do not assign damage yet). Now remove one block for each trap icon in the party, starting with the blocks prepared for the first adventurer, etc. Assign the remaining damage, if any is left. The prevented damage is not dealt.
No matter how much damage is prevented (even if all damage is prevented), the special effect of the trap (no conquering, no spellcasting, skipping the Healing Step, extra damage from poison) is never prevented.
This works the same way every round, regardless of whether some damage was prevented in previous rounds, as long as there are any surviving adventurers with the anti-trap skill.
When planning, you can put two traps here, but you don’t have to choose the order of the traps. In the Trap Step, you can resolve the traps in either order.
Order is important not only because the first trap can eliminate an adventurer (and thus change which adventurer will be affected by the second trap) but also because the second trap is only affected by the anti-trap abilities that remain after the thieves and paladins deal with the first trap.
Example: Suppose we have a thief with 2 trap icons, the paladin with 3 trap icons, and two warriors in between. We played Rolling Stone (4 damage to the first adventurer) and Wall of Fire (1 damage to each adventurer, 1 extra to the last) in our Labyrinth. If we use the Rolling Stone first, then the four damage and also the first damage from the Wall of Fire gets prevented. The paladin will get no damage, the warriors will each get 1, and the thief (as the last line) will get 2 damage. On the other hand, if we use the Wall of Fire first, then its 5 damage gets prevented, and the Rolling Stone does 4 damage to the paladin. In both cases, five damage were prevented and four damage were dealt (but to completely different adventurers).
Nothing. But you still have to discard it after use.