The Imam of my local masjid teaches some ikhwani beliefs and some khawarij ideas like speaking out against the rulers. He takes from Dedew and Turaifi. How should I advise him? He once used the hadith about a sahabi making dua against the imam as an evidence for speaking out against the rulers.

I have answered these questions in my series called "Replying Crystal Clear to the People of Takfir" (in Arabic). When the Sahabi (the companion) corrected the ruler, he did it directly in his presence. As Sheikh Ibn Uthaymeen mentioned, there is an Ijma' (consensus) among the companions of not talking about the ruler behind his back. Whatever occurred happened in the presence of the ruler. Furthermore, these companions held a very high status in society and were close to the rulers themselves. In some of these incidents, the ruler would actually be accompanying the very Sahabi who corrected him; they would be walking hand in hand. Those who quote these incidents to lead people astray completely omit this crucial context. They make it seem as if anybody and everybody is like these companions of high authority and status, who have a high position and a direct relationship with the ruler themselves—which is not the case. So how can we make an analogy like this? They make it seem as if It is everyone's right, even the foolish, and even the people who want to incite and cause corruption in the land. They claim it is their right, without any issue, to come and talk and criticize. If this is not Khuruj, then what is Khuruj? Khuruj never starts except by speech and inciting people against their rulers to cause chaos. So, in regards to you and your question, stay away from these people. It is not as if they are ignorant, waiting for your advice, and ready to change the moment you speak to them. If that were truly the case, then by all means advise them; if they want to listen, they will change. However, most of the time, these people simply want to argue and pull you toward their deviance. Abandon them and warn against them. Barakallahu Feekum.