What is the ruling on calling ‘Ali ibn Abi Taalib, may Allaah be pleased with him, bad names? Who is higher in rank, ‘Umar or ‘Uthmaan, may Allaah be pleased with them?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is not permissible to call ‘Ali ibn Abi Taalib or any other  Companion bad names. Moreover, it is an act of apostasy to criticize him in anything related to the genuineness of his faith or justice, because there are many texts that indicate his virtues and merits. For example, it was reported on the authority of Abu Surayhah or Zayd ibn Arqam that the Prophet, sallallaahu ‘alayhi wa sallam, said that a person who has allegiance to ‘Ali has allegiance towards the Prophet, sallallaahu ‘alayhi wa sallam, himself. Then he supplicated Allaah The Almighty to grant victory to anyone who supports ‘Ali and to cause anyone who antagonizes him to lose. [At-Tirmithi and Ahmad]

Moreover, it was reported on the authority of Sa‘d ibn Abi Waqqaas that the Prophet, sallallaahu ‘alayhi wa sallam, told Ali that his rank in relation to him is similar to that of Haaroon (Aaron) in relation to Moosa (Moses), may Allaah exalt their mention. However, he added that Haaroon was a prophet, whereas the Prophet, sallallaahu ‘alayhi wa sallam, is the seal of the prophets and after him no other prophet would be sent. [Al-Bukhari and Muslim]

In addition to the aforementioned virtues, ‘Ali ibn Abi Taalib was also the first minor to convert to Islam, the cousin of the Prophet, sallallaahu ‘alayhi wa sallam, the husband of his daughter Faatimah and the father of Al-Hasan and Al-Husayn whom the Prophet, sallallaahu ‘alayhi wa sallam, loved very much. When this is the rank of Ali ibn Abi Taalib how could a Muslim dare hate him or call him bad names? Instead, it is an obligation for a Muslim to love him and be loyal to him, without exaggeration or understatement. This is the stance of Ahlus-Sunnah Wal-Jamaa'ah.

In this regard, it is also worth mentioning that there were two Muslim groups who deviated regarding `Ali ibn Abi Taalib . While one of them exaggerated their love and praise for him, followers of the second group declared their enmity towards him. However, Allaah the Exalted guided Ahlus-Sunnah Wal-Jamaa'ah to follow the truth.

As for the part of the question that is related to preference for ‘Umar or ‘Uthmaan Ahlus-Sunnah Wal-Jamaa'ah unanimously agree that ‘Umar is higher in rank than ‘Uthmaan and this was the view of the Companions themselves . Referring to this, it was reported on the authority of Ibn ‘Umar that during the lifetime of the Prophet, sallallaahu ‘alayhi wa sallam, they used to consider Abu Bakr   the best after the Prophet, sallallaahu ‘alayhi wa sallam, then ‘Umar, then ‘Uthmaan . As for the other Companions, they used to consider them of the same rank. [Al-Bukhari]

This citation is used as explicit evidence behind the belief that Abu Bakar is higher in rank than ‘Umar . As for considering ‘Uthmaan higher in rank than ‘Ali there is a difference among the scholars in this regard and this is the view of Ahlus-Sunnah Wal-Jamaa'ah. However, some of the Salaf (righteous predecessors) are of the view that ‘Ali is higher in rank than ‘Uthmaan . This was mentioned by Ibn Hajar . He added that the aforementioned Hadeeth was quoted as supporting the view of the majority of the scholars that ‘Uthmaan is higher in rank than `Ali . 

Allaah Knows best.