Zikr and Dua After Salaah

Reciting tasbeeh-e-Faatimi and Ayatul Kursi after Salaah

Q: Immediately after performing his Fardh and/or Sunnah Muakkadah Salaah, a person is unable to remain seated and recite tasbeeh-e-Faatimi, Ayatul Kursi and other wazaaif on account of some time constraints or traveling. Whilst he is walking to his car, or even whilst driving, can he thus recite Ayatul Kursi, tasbeeh-e-Faatimi and other wazaaif now? Or would it be better to delay it and recite it at another time when he can be completely dedicated towards it?

Sunnah method of dua after fardh Salaah

Q: What is the correct manner of reading the dua after Salaah with regard to reading it loud or soft. Should the dua be made audible (loud) or inaudible (soft)? In our musjid the Imaam starts the duaa loud and reads the first part loud then remains silent and reads the duaa silently, thereafter he reads the ending of the duaa loudly again. Is this correct or is it a bid'a?

Ijtimai Du'a and naseehat after Salaah

Q: After the Fardh Salah the Imam makes Du'a in which many if not the majority of people participate, arguably making it an Ijtimai Du'a. Thereafter, the Imam stands up and gives naseehat to the assembled congregation, thereby delaying the Sunnah prayer. From the end of Salah to the end of the naseehat is between 4-5min. It may be contended that nobody is obligated to sit for the naseehat. However when the majority, if not all the people sit for the nassehat, it makes it
awkward for one or a few individuals to depart to perform their Sunnah as:

(a) People are in the way and get inconvenienced.

(b) Persons draw uncomfortable attention to themselves by getting up and leaving.

Is delaying the Sunnah for this duration or at all permissible?

If not, what is the proof that such a delay is impermissible?