(1) In the question mentioned above you are not sharai musafir, hence it is necessary for you to offer complete four rakat salah at your work place, it is not lawful for you to do qasr.
(2) Answering Azan is mustahab while some other have regarded it wajib, but the reliable and evident ruling is of being mustahab. The ruling for one who is reciting the holy Quran (tilawat) is that if he is reciting in the mosque then he should continue and if he is not in the mosque rather at his home etc, he should stop reciting and answer the Azan. At the time of Azan one should get busy in answering Azan and talking should be stopped, it is not good to continue talking and not answering the Azan. It is wrong to believe that one who talks during Azan will not be able to say Kalma-e-Shahadah at the time of death.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband