Are the compilation of the Qur’aan and the first adhaan for Jumu’ah forms of bid’ah (innovation)?
Question

                if bidah is wrong· then what about the quran being compiled? and other things such as umar introducing something in the azan? please make this clear as some people say good bidah is allowed· relating it to one of the prophets hadith?
Praise be to Allah.For a correct definition of bid’ah and guidelines concerning it, please see Questions no. 864, 205, 10843. 
With regard to what you mention about Abu Bakr compiling the Qur’aan, this is not bid’ah, rather it is Sunnah such as the Prophet (peace and blessings of Allaah be upon him) enjoined us to adhere to when he said: “I urge you to adhere to my Sunnah and the Sunnah of the Rightly-Guided khaleefahs after me.” (Narrated by al-Tirmidhi, 2676; Abu Dawood, 4607; Ibn Maajah, 42. This hadeeth was classed as saheeh by al-Tirmidhi, by al-Haakim, 1/177; and by al-Albaani in Saheeh al-Jaami’, 2549, from the hadeeth of al-‘Irbaad ibn Saariyah). This is one of the Sunnahs of the Rightly-Guided Khaleefah Abu Bakr al-Siddeeq (may Allaah be pleased with him). 
Bid’ah means seeking to draw close to Allaah by means of acts of worship for which there is no precedent (in sharee’ah). The Qur’aan was compiled in people’s hearts and it was compiled on tablets kept by some of the Sahaabah. Compiling all of it in one place or on one tablet does not involve anything that is to be denounced. 
Zayd ibn Thaabit said – when Abu Bakr delegated him to collect the Mus-haf – I sought the Qur’aan and I gathered it from pieces, i.e., leaves, patches of leather, shoulder-blades of sheep and camels, leaves of palm trees, and the hearts of men. 
Al-Qaadi Abu Bakr al-Baaqillaani mentioned the justification for the action of Abu Bakr, the five most important points of which were: 
1 – That the Messenger of Allaah (peace and blessings of Allaah be upon him) did not do that for a reason, and Abu Bakr did it because there was a need for it. 
2 – Allaah referred in the Qur’aan to al-Suhuf al-Oola (the former Scriptures – al-A’laa 89:19], and He stated that Muhammad (peace and blessings of Allaah be upon him) had something similar in the aayah (interpretation of the meaning]:  
“reciting (the Qur’aan) purified pages [purified from Al-Baatil (falsehood)].
Wherein are correct and straight laws from Allaah”
[al-Bayyinah 98:2-3]
So this [action of Abu Bakr] was following that which was prescribed by Allaah and His Messenger. 
3 – By doing that, their intention was to fulfil the words of Allaah: 
“Verily, We, it is We Who have sent down the Dhikr (i.e. the Qur’aan) and surely, We will guard it (from corruption)”
[al-Hijr 15:9]
It was preserved with Him, and He told us that He would preserve it after it had been sent down. Part of His preserving it was His enabling the Sahaabah to gather it and to agree upon how its spelling and punctuation were to be regulated.
4 – The Prophet (peace and blessings of Allaah be upon him) had scribes to whom he dictated it, so that everyone would understand from this that it should be written down and preserved on sheets. If Allaah’s guarantee to preserve it meant that the ummah would have nothing to do with it, the Messenger of Allaah (peace and blessings of Allaah be upon him) would not have had it written down after Allaah had told him of His guarantee to preserve it. But it is known that the way in which Allaah has preserved it is by causing us to preserve it and making that easy for us, and showing us how it is to be written down. 
5 – It is proven that the Prophet (peace and blessings of Allaah be upon him) forbade traveling with the Qur’aan to the land of the enemy. This indicates that it was written down and that the people used to take it with them when they travelled. 
Abu Bakr ibn al-‘Arabi said: this is the clearest evidence for anyone who studies the issue.                                                                  
See Ahkaam al-Qur’aan, 2/612 
With regard to your saying that ‘Umar added “something new” to the adhaan, we know nothing of that. But perhaps you were referring to the fact that ‘Uthmaan added the first call to the Jumu’ah prayers. This is correct, because at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him), there was just one adhaan, but when ‘Uthmaan became khaleefah and Madeenah became larger, ‘Uthmaan thought that the call for Jumu’ah should be given before the time, so the people could get ready for the prayer. This is what is called the first adhaan.
It was narrated that al-Saa’ib ibn Yazeed said: At the time of the Prophet (peace and blessings of Allaah be upon him), Abu Bakr and ‘Umar, the first call on Friday used to be when the imaam was sitting on the minbar. But at the time of ‘Uthmaan (may Allaah be pleased with him), when the number of people increased, he added the third call. According to one report, ‘Uthmaan gave orders for the first call. According to another report, the second adhaan was enjoined by ‘Uthmaan. There is no contradiction here, because it is called the third call in the sense that it was something added; the first in the sense that it comes before the adhaan and iqaamah; and the second in the sense that this is an adhaan given in addition to the real adhaan, which was given in al-Zawraa’. Abu ‘Abd-Allaah – i.e., al-Bukhaari – said that al-Zawraa’ was a place in the market of Madeenah.
 Narrated by al-Bukhaari, 870. 
This adhaan is not a bid’ah or reprehensible innovation, rather it is one of the Sunnahs of the Rightly-Guided Khaleefah ‘Uthmaan ibn ‘Affaan (may Allaah be pleased with him), which the Prophet (peace and blessings of Allaah be upon him) urged us to adhere to when he said: “I urge you to adhere to my Sunnah and the Sunnah of the Rightly-Guided khaleefahs after me.” 
Moreover there is a sound reason behind it, which is to alert the people to the fact that the time of prayer is at hand. And it is worth noting that there are no rulings attached to this (first) adhaan, such as the prohibition on buying or selling or the obligation to go to the mosque, and that ‘Uthmaan was wise to have this call made in the marketplace and not in the mosque. This is no more than an alert to the people, to let them know that the time for prayer is at hand, because the houses were far away and far from one another, as mentioned above. 
Hence it was narrated that ‘Ali (may Allaah be pleased with him) did not do that in Kufa because there was no need for it. 
And Allaah knows best.