My friend is advised to have a respitory system. what all should be checked?

Sorry but: This is a bit of a strange question. If you mean a respiratory system exam, firs you need to be asked a bunch of good questions and really listened to for whatever it is that is your problem. Then you should be listened to very carefully with the stethescope. It is really hard to say what else needs to be checked without knowing what your problem is. That will be determined by answers and exam.

Lungs: Turns out we all have a respiratory system - our lungs! so i suspect someone advised your friend to get his/her lungs checked out, probably due to a cough or shortness of breath, perhaps wheezing. Any family doc can listen for signs of common colds, bronchitis, pneumonia, asthma, copd, pneumothorax, etc. If your friend smokes, best decision health-wise is to quit asap.

Respiratory system: Respiratory system refers primarily to our breathing system, ie nose, throat and lungs. As such, one would want to get an xray of the lungs and possibly the sinuses. Since you have a cough and cold one would be concerned about pneumonia, bronchitis or sinusitus. Have your doctor evaluate you.