Should I Kill Crestfallen Warrior?
As He Doesn't Drop Any Item nor Does He Have Any Effect on Other Npc's Story, You Don't Need to Worry About Killing Him by Kicking Him off Cliff as His "Full...
As he doesn't drop any item nor does he have any effect on other NPC's story, you don't need to worry about killing him by kicking him off cliff as his "full reward" is only his souls. Which is to say, there are no penalties for killing him, and you can snag a quick 1000 souls in the process!
Is it better to kill Lautrec?
After defeating him you can find his corpse, outside the chamber of the princess in Anor Londo, containing his entire suit of armor. Killing him without following the above will only grant you the Ring of Favor And Protection and 5 Humanity, you will not be able to obtain his or Anastacia's armor.
What happens if you kill the guy at firelink shrine?
It resets the NPC aggro status. It also resets your soul wallet to 0 status. You end up killing him later anyway. He eventually goes hollow and moves down to the New Londo Ruins area.