Assalam ailkum wa rahmatullah wa baraktoh, I was praying in a Turkish mosque and found the meuzzin saying the duaa (supplication) after the azan out loud. Is this permissible?
and after they finish the prayer they take a special moment for tasbeeh(praising God) and also the meuzzin says a few things. They say this according to the Hanafis but is there any proof for these acts?

The permissibility of making dhikr and du'aa` out loud is established by the Qur`an and sunna and the practice of the early and late generations of Muslims. A number of scholars authored books on this issue; these include al-Suyuti's treatise Natijat al-Fikr fi al-Jahr bil Dhikr and imam Abu al-Hasinat al-Laknawy's book Sahet al-Fikr fi al-Jahr bil Dhikr among others.

Nothing has been mentioned in the source texts obligating the manner of invoking peace and blessings upon the Prophet (peace and blessings be upon him), whether silently or audibly. The matter is capacious and when Allah legislates a matter in a general fashion and it can be done in more than one manner, it must be interpreted in light of its capaciousness. It is invalid to restrict it to a particular manner except in the existence of substantiating proof.

Making du'a` and invoking greetings of peace upon the Prophet after the adhan (call to prayer) is an established sunna that was mentioned in authentic reports. Abdullah ibn Umar ibn al-'As (may Allah be pleased with them) related that he heard the Prophet (peace and blessings be upon him) say, "When you hear the muezzin (caller to prayer) make the adhan, repeat what he says after him and then invoke peace and blessings upon me.

For whosoever invokes peace and blessings upon me once, Allah sends blessings upon him ten-fold. Then ask Allah to grant me al-waseela — it is a rank in Paradise that is reserved for only one of the servants of Allah and I hope to that person. Whosoever asks Allah to grant me al-waseela will earn my intercession" [Reported by Muslim, Abu Dawud, at-Tirmidhi, and an-Nisa`i].

There are some reports from the Prophet that evince the practice of invoking peace and blessings upon him audibly after the adhan. Abu al-Darda` (may Allah be pleased with him) narrated that upon hearing the adhan, the Messenger of Allah would say, "O Allah! Lord of this comprehensive call and current prayer, grant Muhammad his request on the Day of Judgment." Those around him would hear him making this supplication, and he liked them to supplicate with the same after the adhan.

He said, "Whosoever supplicates with the same when he hears the mu`ezzin calling out the adhan, the intercession of Muhammad, peace and blessings be upon him and his family, becomes mandatory upon him on the Day of Judgment"[Reported by at-Tabari in his Al-Mu'jam Al-Kabeer].

The Divine injunctions in the Qur`an on making dhikr in general and after prayers in particular are general. These include: O ye who believe! Remember Allah, with much remembrance; and glorify Him morning and evening. [Qur`an 33: 41-42] And keep yourself content with those who call on their Lord morning and evening, seeking His face. [Qur`an 18: 28] When ye have performed the prayers, remember Allah, standing, sitting down, or lying down on your sides. [Qur`an 4: 103]

A general injunction must be implemented as such until something comes to restrict it. Some ahadith indicate the permissibility of making dhikr audibly after prayers. Bukhari and Muslim reported that Ibn Abbas (may Allah be pleased with them both) narrated that during the Prophet's lifetime, voices would be raised in dhikr after the obligatory prayer. He said, "I would know that prayers had finished when I would hear dhikr being made." In another wording of the hadith, he said, "I would know that the Prophet had finished praying when I would hear the takbir (glorification of Allah)." Those scholars who take the apparent meaning of the hadith, maintain the permissibility of making dhikr audibly after prayers while those who interpret it as the Prophet teaching the congregants to make dhikr, maintain that it is preferable to make dhikr after prayers silently; the permissibility of both audible or silent dhikr after prayers is acknowledged by both parties.

Abu Hurayra (may Allah be pleased with him) narrated that the Messenger of Allah (peace and blessings be upon him) said, "Allah the Almighty says, 'I am as my servant expects me to be. I am with him when he makes mention of Me; if he makes mention of Me to himself, I make mention of him to Myself. If he makes mention of Me in an assembly, I make mention of him in a better assembly. If he draws near to me a hand span, I draw near to him an arm's length and if he draws near to me an arm's length, I draw near to him a fathom's length. If he comes to me walking, I go to him at speed" [Bukhari and Muslim].

The luminary Ibn al-Jasriy wrote in Muftah al-Hisn al-Hasin, "This hadith indicates the permissibility of making dhikr audibly, contrary to the opinion of those who forbid it." The hadith scholar al-Suyuti wrote in Natijat al-Fikr fil Jahr bil Dhikr, "Mentioning someone in an assembly is always audible."

Al-Suyuti mentioned in his treatise twenty five ahadith all of which point to the permissibility of making dhikr audibly. After mentioning the ahadith, he said, "Upon contemplating the ahadith, one will note there is no aversion whatsoever to audible dhikr; rather, they indicate its recommendation either explicitly or implicitly. Their inconsistency with the hadith stating that the best kind of dhikr is that which is made silently, corresponds to the inconsistency between the ahadith on reading the Qur`an audibly and the ahadith on reading it silently, in comparison to the hadith on giving alms in secret. In reconciling between the ahadith, An-Nawawi mentions the virtues of both. He said that making dhikr silently is better for a person who fears hypocrisy or if his audible dhikr may harm others who are either praying or asleep. Otherwise, audible dhikr is better because it involves greater action, its benefit transcends to those who are listening, it stirs the heart of the invoker and energizes his determination to contemplate. Moreover, it drives away sleep and increases energy. Some people have said that it is recommended to recite the Qur`an audibly at some times and silently at others. This is because a person who recites the Qur`an silently may become bored and so resorts to reciting it audibly while a person who recites the Qur`an audibly may become fatigued and so resorts to reciting it silently.' End of quote. The same is applied to dhikr and in this manner we reconcile between the inconsistent ahadith."

The best thing to say on this matter are the words of imam al-Tahawi in his meta-commentary Maraqi al-Faleh on the topic of reconciling ahadith and the opinions of scholars who differed on the preference of silent or audible dhikr and du'a`. He said: "Matters differ due to the disparity between people, situations, time, and goals. When a person fears hypocrisy or when audible dhikr harms another, silent dhikr is better. Otherwise, it is preferable to make dhikr audibly." Muslims must not make this a cause of strife and dissonance. Objection is not for issues over which there is a difference of opinion. The right thing to do is to let people act spontaneously: whoever wishes may make dhikr audibly and whoever wishes may make dhikr silently.

This is because the matter of dhikr and du'a` is capacious and the important thing is that a Muslim is to do what he finds in their heart. No one is entitled to object to another's practice as long as the matter is capacious.