The hadiths that relate to the Ummah's division have been cited and narrated through various chains of Sunni and Shia narrators.
All of them have spoken of the division of the prophet’s ummah after him and the establishment of new Islamic sects. In whole, it can be claimed that these hadiths somewhat bear tawatur in meaning and in the message they convey. At least one of these hadiths is completely accepted by the Muslim scholars, its chain of narrators being authentic and connected to the infallibles.
Unfortunately, most of the time after prophets would pass away their people would turn away from their religion's true path. Because the prophet possessed the power to see the future of his nation, he has informed us that such thing would happen to the Muslim Ummah as well (in the hadiths of ‘the division of the ummah’). Both Sunni and Shia narrators have narrated these ahadith through various chains of narrators. These ahadith are narrated in Shia hadith sources like Khisal of Sheikh Saduq, Tafsir Ayyashi and Ihtijaj of Tabarsi. These ahadith may differ in the words and phrases used in them but share the same message making them mutawatir in meaning and in the message they convey (a mutawatir hadith is one that has been narrated so much by different narrators that one becomes sure it is something the imams have said and that it is impossible for all of the narrators to have lied or been mistaken in their narration).
According to these ahadith the Prophet of Islam has predicted that Muslims will be divided in to 73 sects after his passing.
The most authentic hadith in this regard has been mentioned in Kuleini’s book of Kafi, the hadith is by Imam Baqir (as) and we will examine this hadith as an example:
The chain of narrators: "مُحَمَّدُ بْنُ یَحْیَى عَنْ أَحْمَدَ بْنِ مُحَمَّدِ بْنِ عِیسَى عَنِ ابْنِ مَحْبُوبٍ عَنْ جَمِیلِ بْنِ صَالِحٍ عَنْ أَبِی خَالِدٍ الْکَابُلِیِّ عَنْ أَبِی جَعْفَرٍ(ع)"
There are different categories for the ahadith in terms of their narrators. If the narrators are all Shia and have been described as thiqah (trustworthy) then hadith scholars name it a 'Sahih hadith' (correct and authentic). Obviously if the narrators of a sahih hadith are all among the greatest and most learned scholars of their time the authenticity will increase and the hadith will be utterly accepted. The hadith that has been narrated from Imam Baqir (as) has narrators that have been among the greatest of their time. For example, one of the narrators Mohammad Ibn Yahya, is one of the greatest scholars of his age. When describing him, Najashi (a Muslim scholar that has a book on narrators) says: "He was the greatest of Shia scholars of his time and he is utterly trustful". He also describes Ahmad Ibn Mohammad Ibn Isa saying: "Aboujafar (Ahmad ibn Mohammad ibn Isa) is the Sheikh of Qom's scholars and he is the most learned of them in jurisprudence". Hasan Ibn Mahbub is also among the trustworthy narrators and is considered one of the Ashabe Ijma’ (a narrator which every hadith he narrates is accepted, no matter who the other narrators before him are). Two other of the narrators, Jamil Ibn Saleh and Abu Khaled Kaboli, are also great scholars of their time.
Therefore the hadith is totally accepted by hadith scholars in terms of it's narrators.
This hadith has been issued in interpretation of verse 29 of Surah Zomar; Imam Baqir (as) says: "The Jews divided into 71 sects after their prophet passed away, and only one of these sects will go to heaven while the rest will be sent to hell. The Christians also divided into 72 sects after Prophet Isa, and only one of the sects will go to heaven. As for the Muslim Ummah, it will divide into 73 sects in which 72 of them will go to hell. There are 13 sects among the 73 which have love and affection towards us, the Ahlul-Bayt and accept our wilayah but only one will enter paradise. Therefore these twelve of these 13 and the other sixty sects will all go to Hell."
Conclusion: Both the chain of narrators and the contents of the hadith are correct and authentic and corroborated by other hadiths in this field. It must be noted that most of these ahadith have mentioned that the sect that will go to heaven are the followers of Imam Ali (as).
To get the answers to the other questions you had, refer to the following subjects:
1- Question 192 (website: 2381) (The reasons for the emergence of other Islamic sects).
2- Question 4932 (website: 5182) (The motives behind the emergence of different sects).
 Mohammad Hosein Tabatabai, Al-Mizan (Farsi translation), vol. 3, pg. 588; Yaqub Jafari, Tafsir Kawthar, vol. 3, pg. 443.
 Muhammad Baqir Majlisi, Biharul-Anwar, vol. 28, pg. 4.
 With help from the Dirayatul-Nur software (the section on hadithic terms).
 Najashi, Rijal Najashi, pg. 353.
 Ibid, pg. 83.
 See: Rijal Najashi, pg. 556.
 See: Rijal Najashi, pg. 127 and Rijal Kashi, pg. 10.
 The hadith is probably referring to Shia sects other than the twelve imamer Shia sect.
 Muhammad ibn Yaqub Kuleini, Kafi, vol. 8, pg. 224.
 Biharul-Anwar, vol. 28, pg. 2 (chapter Iftiraqul Ummah badal Nabiyy ‘The division of the ummah after the prophet’).