How can I get rid of the problem of self-admiration and arrogance that Satan casts into my soul regarding my actions, and even my understanding of some words?

The cure for conceit is to be mindful that understanding is a blessing from Allah Almighty, and to be grateful for it. If you are mindful that this is a blessing from Allah and you are pleased with it, then it is not the blameworthy conceit, because the prohibited conceit is the magnification of the blessing while forgetting that it is from Allah Almighty. Also, one should continue learning and studying, and be mindful of the reward therein, and be keen for knowledge to be sought for the sake of Allah Almighty. Imam Al-Shafi'i explained that the fear for one's deeds from conceit comes from considering the satisfaction of whom you seek, what reward you desire, what punishment you dread, what well-being you thank for, and what tribulation you remember. For reflecting on these qualities diminishes the deed in one's eye. Conceit is the magnification of the blessing while forgetting that it is from Allah, and it is treated by knowing that Allah Almighty is the Originator and Giver of all blessings, and that the servant creates neither benefit nor harm. One must be mindful of the danger of conceit and that it is a cause of destruction, as stated in the saying of the Prophet (peace and blessings be upon him): "And three are destructive: covetousness that is obeyed, stinginess that is followed, and a person's admiration of himself." And that conceit is greater than sins, for if we did not sin, we would fear for ourselves something greater than that conceit. And that conceit may lead to being swallowed by the earth, as happened to a man who was walking in fine clothes, pleased with himself. And Ibn Mas'ud said: "Destruction is in two things: despair and conceit."