1) Although reciting words of praise and glorification upon hearing the word "Allah" is not obligatory, it is better to recite words of glorification upon hearing God’s Glorious name, as a demonstration of respect.
2) When the name of the Holy Prophet (peace be upon him) is mentioned for the first time in a gathering, it is Wajib for all listeners to recite Durood once in that gathering. After reciting it once, if the Holy Prophet’s Name (peace be upon him) is mentioned again in the same gathering, it is mustahab to recite Durood.
3) Allah Ta'ala has mentioned sending salam upon other Prophets (peace be upon them) many times in the Holy Quran. Therefore, it is better for the listener to send salam upon them when the name of a Prophet (peace be upon him) is mentioned.
4) The scholars have written that it is mustahab to pray for the Sahabah and Sahabiyat (may Allah be pleased with them all) by saying "radiyallahu anhu" when hearing their names.
5) "Rahmatullahi alayhi" is a dua. It is not obligatory to pray for a respected elder by reciting this phrase when their name is mentioned. However, if this dua is made for them, it will be a form of recognition or compensation from us for their scholarly services.
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دلائل:
القرآن الکریم:(سورۃ الاحزاب، رقم الآیة:56)
اِنَّ اللّٰهَ وَمَلٰٓئِكَتَهٗ يُصَلُّوۡنَ عَلَى النَّبِىِّ ؕ يٰۤاَيُّهَا الَّذِيۡنَ اٰمَنُوۡا صَلُّوۡا عَلَيۡهِ وَسَلِّمُوۡا تَسۡلِيۡمًا o
القرآن الکریم :(سورۃ الصافات، رقم الآیة: 119-120)
وَتَرَكْنَا عَلَيْهِمَا فِي الْآخِرِينَ o سَلَامٌ عَلَى مُوسَى وَهَارُونَ o
معارف السنن:(292/4، ط: مکتبة البنوریة)
قال في شرح المنيه ولو تكرر ذكره عليه الصلاة والسلام في مجلس واحد قال في الكافي لم يلزمه الا مرة واحدة في الصحيح.
و فیه ایضاً: (292/4، ط: مکتبة البنوریة)
وفي تقريب النووی و شرحه للسيوطي:
و كذا ينبغي المحافظة على الثناء على الله سبحانه وتعالى كعز وجل و سبحانه و تعالى وشبهه الخ۔
کذا فی فتویٰ دارالعلوم دیوبند:
رقم الفتوٰی: 58081 رقم الفتوٰی: 602455
Allah the Almighty knows best.
Darul ifta Al-Ikhlas, Karachi.