My 2008 Ford Fiesta makes a sound like air coming out of a bicycle pump (in my opinion) when going over speed bumps. I noticed the rubber buffer on the back right shock is damaged. Can you help me diagnose the problem? Is it serious? From the little tests I have done, the car seems to be running fine.
As Paulster2 stated in the comments, good shocks will make a whooshing type noise when going over speed bumps, which is created by the fluid rushing through the shock valves. This is completely normal.
Also, considering the age of your vehicle, it is highly unlikely that your shocks are blown out unless you have been driving on extremely rough roads for long periods of time, or live in an extreme weather environment (think Death Valley with sand storms and a pinch of locusts type of extreme).
Rather than noise, the best way to see if your shocks are blown out is feel. Shocks are used to dampen the movement of the spring. A un-dampened spring (spring without a shock) will bounce up and down, slowly oscillating until it comes to a rest. You can test the shock by bouncing all your weight on one corner of the car. If the spring compresses, releases, and stops moving, the shock is functioning properly, if it compresses, releases, and keeps on bouncing without you adding more weight, the shock is no longer restraining the movement of the spring, and needs to be repaired or replaced.