Currently, you cannot pick up any projectile thrown by an NPC (or arrows). My solution is that you can pick up all NPC thrown projectiles, such as Spears, throwing axes, etc. Arrows, darts, and crossbow bolts have broken forms. You can repair them with wood planks (darts and arrows) or iron (crossbow bolt). This would give you a repaired arrow. These deal less damage than Normal ones. 40% of arrows/darts/bolts NPCs shoot would be unable to be picked up (unrepairable). 40% would be broken, and 20% would be in good condition (normal arrow). Broken arrows cannot be shot. Arrows you shoot have a 30% unable, 40% broken, 30% good condition.
Currently you cannot ride NPC horses or mounts. Why not? You would have to re-tame it in order for it to get used to you and you can ride it then.