secondary air pump
 

Hello everyone!....new to the site! My question is in reference to the secondary air pump. Driving a manual 3.0i and began to see the SES light approx. a year ago intermittently on/off. After diagnostics the stealer said the pump needed replacement. My questions are these:

1) I can still hear the pump operate first 30 sec. of cold start-up with no change in sound since purchase....does this mean the whole pump needs replacement or is there a valve that might not be functioning?

2) Am I damaging my cat. converter and o2 sensors if the pump is not functioning like it should?

Not sure what you mean here. Is this before or after the dealer replaced the pump? Is it continuously running? It's normal to hear the pump run on cold starts but it should turn off after a short while. The actual duration depends on how cold the engine is.
I don't think there will be any damage as in fouling of cat or sensors. Secondary air system is only to reduce emissions on cold start. No air just means you'll fail emissions tests (if you are required to have them).

I didn't replace the pump and it does shut off after a short while. If I can hear it functioning how can it be bad??? Is there a valve that could be possibly closed???

Yes, the check valve on the manifold could be malfunctioning or there could be a leak in the vacuum line that operates the check valve or there could be a problem with the solenoid valve that operatates the vacuum line.

I'm having the same symptoms right now with my 330xi. I'm waiting for it to get warmer here before I take a look at it.