(2) Today I went to English toilet in my office, after I finished off with toilet; within seconds again toilet came and later I realized that it was semen like material or semen that came out but I offered Salah in that condition since I was in office and cannot go for ghusl. Is ghusl compulsory in this situation and I became profane?
بسم الله الرحمن الرحيم
(1) It is enough to do taubah and istighfar.
(2) If you are sure or there is great probability that the semen was discharged with lust then ghusl was wajib. It was not lawful to offer salah in that state. You should reoffer all the salah offered in that state besides doing taubah and istighfar.
Allah knows Best!
Darul Uloom Deoband