Our leading scholars do not accept the claims of abrogation of many verses in Quran except one verse which is in Sura al-Mujadalah , verse 12 ( O you who believe: Give a charity ( Sadaqa) when you consult the messenger in secret) before doing that) Sura 58, verse 12.
'This verse is the only verse in Quran which was abrogated because no one from all Muslims emplimented it except Ali Ibn Abi Talib (AS).
Other verses which have been claimed by many as abrogated are not really abrogated. More details are in Tafseer al-Bayan by Sayyed al-Khoei.
Quran was gathered by Imam Ali (AS) under direct instructions from the Prophet Muhammad (SAWA).
The Qur'an was compiled in chronological order by Imam Ali (AS) as we read in our books. Qur'an was also compiled in the present order by Imam Ali (AS) according to the orders of the Prophet (SAWA). The Prophet (SAWA) used to order Imam Ali (AS) to put every new verse in the place where the Prophet used to order, so it was not according to chronology but the wisdom and the aim of guiding people to the Truth.