In our office mosque, we usually read from a hadith book at the end of Asr prayers. Sometimes we read loudly while some of people are still praying, this may cause disturbance to the worshippers. What is the ruling here? Is this recitation allowed?
To read, to teach, to make a speech etc. are allowed inside a mosque. This is a long practice since the first mosques of Medina. I've come across no scholar to call these acts Bid'ah or innovation inside deen.
I had the chance to face both the ends of the situation that you've mentioned in your question.
When someone is reciting or reading or making a speech loudly it is very hard to concentrate in the prayer. It hampers the tilawat and reciting inside the salat.
On the other hand when someone is saying his prayer in such a place which is close to any gathering inside the mosque it creates a very unlikely situation. Where several dozen people wait for an individual to complete his salat.
In terms of fatwa, it is not permissible for anyone to inflict harm or inconvenience on others. The resolution of this situation is more of a common sense or good manner rather than fatwa or jurisprudence.
If we have any such program
(ex. bayan, talim etc.)after salat, then we should start our program after an average time has elapsed after the end of the congregational prayer. So, that average musalli can easily end their prayers and then attend the program. Also we should keep in mind that if it is a small compound, then the sound of our program should not hamper those individuals who are at a corner, engaged in their regular amal
(such as tilawat, dhikir, nafl salat etc.)
If I am interested to pray nafl salat for a longer period of time, then I should make room for others and should not hamper the programs taking place. The best thing would be to attend those programs if enough time is in hand, then complete my individual amal. If that's not possible then I should go to a side of the mosque and say nafl salat. For instance if I know that in this part of the mosque there is a regular gathering, then its better to move in advance to a convenient place so that none feels waiting for me.