SubhanAllah … This thread is not going very well …
The prayers which do not have nafl after them i.e. Fajr and Asr have a very good reason for this. Also, it is not true that nafl can be offered anytime.
Ok … offering any prayer nafl or qaza after fajr fard is prohibited, because this was the time when pagans used to worship the sun on it’s rising. After Fajr until a point when the sun is clearly above the horizon offering any prayer is not allowed. After this time the nafl prayer ishraq or doha can be offered. Then any nafl can be prayed until a few minutes before high noon, which is called zawal time - at zawal time it is prohibited for any prayer - (not Qur’an or tasbeeh, just salat) - again for the same reasons. Again it is prohibited to offer any prayer after 'asr until the sun has set.
Some people offer tahiyatul-masjid which is also nafl whenever they enter the masjid many do this before dhuhr i.e. during zawal time and also just before the maghrib prayer both are wrong because these are the wrong times to offer any prayer.
A hadith mentions that we should avoid praying between the two horns of the devil. Otherwise if we start nafl prayer before the azan has started there is nothing wrong with this (but we need to be cautious of zawal times of high noon and when the sun is in the middle of setting), we should not offer any prayer when the azan has started. Many masjids do their azans 15 minutes before jamat or something like that, but azan prayer marks the end of one time and the beginning of another, so really we should wait for the azan before doing the sunnah of the next prayer.
I hope this is clear.
