To directly answer your questions:
- No, you do not need to replace it. Many cars exist without an ARB (anti-roll bar, also know as a sway bar). The purpose is to help prevent the body from rolling excessively. Without it, you will notice the car rolls left/right more when cornering. Unless you enjoy pulling g's through corners--and some of us do--this isn't strictly bad.
- Anytime you replace a component that is mirrored (ex. drop links, headlights, control arms) you replace them in pairs. If the first one broke, the second isn't long for this world.
- You can use junkyard parts, but drop links (end links) typically have ball joints or bushings on them. These are wear items, so using a junkyard part means you take the risk that the part is at or near the end of its life. If you're particularly savvy, you might know what to look for on a drop link to determine how worn it is, but it's better to simply replace it with a new part. How many miles did you get on these ones? 63,000? If I told you that for $75 you could drive another 60,000 miles would you risk spending $30 for parts that may get you anywhere from 0 to 60,000? You're paying $0.00125 per mile. Drive a little lighter and you'll save more in gas (and the parts will last longer). No reason to cheap out here.
As for ARBs in general:
Background: Under ideal conditions, the body remains parallel to the road at all times; however, cornering tends to create a moment about the vehicle center of mass, which is often above the roll center (don't worry too much about terminology) of the vehicle. As a result, you end up with the body rolling toward the outside of the turn.
Purpose: ARBs are designed to control how the body rotates about the vehicle X-axis (runs forward/backward) relative to the road. They work by linking the travel between the left and right side of the vehicle. This actually removes some of the independent nature of the suspension, since now the left and right sides have a semi-rigid connection. As a result, upward travel on the left front shock will induce a lesser degree of travel in the right front shock. Because body roll manifests as (nearly) equal and opposite travel on the left and right suspension components, this linking reduces the travel, keeping the body from rolling excessively.
Benefits: Aside from high-frequency turning, it makes little difference to most driving conditions and instead exists as a comfort feature. It's nice when the car doesn't roll violently from side to side when entering and exiting turns at speed. It also matters when you go from turn to turn because even though the center of mass doesn't move much (really, it doesn't), that small motion amplified by higher frequency turning leads to very high induced forces. In fact, the force is proportional to the frequency squared:
F ∝ Aω²
If you'd like a proof, I can edit my answer to include it. Either way, it only matters significantly when you go from turn to turn quickly.
Detriments: As I said before, it works by linking left and right suspension travel. This is fine for obstructions like speed bumps where travel is nearly equal anyway, but it can actually induce body roll over other obstructions, like potholes. This is because one wheel is forced to travel much farther than the other and the ARB links them, causing the other wheel to travel, leading to body roll. From a pure comfort perspective, it actually contributes negatively under most driving conditions because of this.
Thoughts: Others have made this sounds like quite the life-or-death situation, but it's really not. You can remove the ARB with little consequence, though that's not the case for most suspension components. That said, just fix it. You probably don't even need to remove the wheel and it's typically just a bolt-on component.