Firstly they [strata managers] are not an owner, so do not have any voting or speaking rights.
If the strata manager is asked a question then they are entitled if not expected to answer. The only reference to “speaking rights” that I can find in the NSW Act refers to owners who attend meetings but must get the permission of the committee before speaking. Also, if the strata mangers are holding proxies, they are entitled to vote except on matters relating to their contracts or remuneration.
Conflicts of interest do not negate votes – they simply have to be declared.