Question: Can we read durood shareef in any dua we make (i.e. after salah and any other occasion)?
Answer: One should always start and end supplications with Al-Salaatu-3ala-n-Nabiyy. Apart from that one should do as much as one can of it during the day along with other dhikr. A nice one is "Allaahumma Salli ^alaa Sayyidinaa Muhammad wa ^alaa 'aalihii wa SaHbihii wa Sallim."
... and Allah knows best.