Is it permissible for a Muslim to describe other Muslims using abusive language such as "Satan" and "Khawarij"? And what is your advice to one who does so? Is there a sin in it?

A Muslim must guard his tongue, for Allah records every word, and a person may be cast into the Fire by a word they gave no thought to. The Prophet, peace and blessings be upon him, warned against the harvests of the tongues. Among the sayings of the scholars in this regard are: "It is incumbent upon the intelligent person to maintain silence until it becomes necessary for him to speak," and "Guarding the tongue is the pivot, and it is the master of a servant's affair."

As for describing a person as a devil or a Khariji: 1. Describing him as a devil: This is a forbidden insult and abuse, and reviling a Muslim is unequivocally فسق (disobedience/sinfulness). 2. Describing him as a Khariji: This is an accusation of misguidance. There are two scholarly opinions regarding the تكفير (declaring someone an infidel) of the Khawarij. This term should not be used unless the person agrees with the fundamentals of the Khawarij, including: Flaws in the issue of faith, as they believe that faith neither increases nor decreases, and they declare the perpetrator of a major sin an infidel. Drawing the sword against Muslims, not against disbelievers. Exaggeration in declaring others infidels and following ambiguous evidences, applying verses pertaining to disbelievers to believers.

One must be cautious of insulting people and accusing them of things they are not, especially falsely describing them as Khawarij due to a difference in methodology or opinion.