Is it obligatory to observe the proper sequence between the Dhuhr and Asr prayers when combining them, meaning is it obligatory to begin with Dhuhr first? And is it permissible to perform the Sunnah prayers before and after Dhuhr and the Sunnah prayer before Asr after combining them?

It is permissible for a person to pray Dhuhr behind someone praying Asr, and then pray Asr. As for the post-Dhuhr Sunnah (definition) (Sunnat al-Dhuhr al-Ba'diyyah), it is permissible to make it up after Asr if the two prayers are combined (either by advancing or delaying), and continuity is not obligatory in a delayed combination. However, the pre-Asr Sunnah (Sunnat al-Asr al-Qabliyyah) is not made up once its time has passed, according to the Hanbalis, because it is not among the emphasized regular ( rawatib ) prayers.