In theory, carbon fiber could stop a bullet, but Kevlar® or other aramid fiber has more flexibility and impact resistance. Besides, Kevlar® is a more cost-effective option for bulletproof armor.
Carbon fiber does offer a high level of protection against some objects. You'll often see race car drivers use it for protection because it disperses the impact of forces. But when it comes to bullets, you'll need many layers to stop it.
Watch this video to see how carbon fiber composite fairs against bullets.
However, carbon nanotubes can withstand bullets. Nanotubes consist of carbon atoms bonded in repeating hexagonal patterns to create a hollow cylinder. These nanotubes can absorb the energy from ballistic missiles better than carbon fiber and, in some cases, even Kevlar®.
At its most basic form, carbon fiber is carbon graphite, which will last virtually forever. The material is typically not photo-degradable or biodegradable. However, some factors do influence its durability, like its matrix. Furthermore, the intense use of composites and environmental factors could affect its durability and potential applications. In general, scientists anticipate carbon fiber parts to last for over 50 years.