How can we differentiate between the statement of Sheikh Ibn Uthaymeen regarding the obligation of having certainty in faith and your statement that whoever's Islam is established with certainty is not exited from it by doubt, especially in the context of doubting the validity of one's faith and considering it a form of disbelief?

Certainty and conviction do not contradict Waswasah (whispers/obsessive thoughts), but they do contradict doubt. Exception in faith, if it stems from doubt in its origin, is disbelief (kufr), because faith is conviction and doubt negates it. Waswasah is what assails the heart without choice, and disliking it indicates pure faith. Doubt is the opposite of certainty; it is hesitation between two things, and a servant cannot be a believer if they fall into such doubt. The rule "Whoever's faith is established with certainty does not exit from it by doubt" means that faith does not disappear with doubt, but rather through the establishment of proof and the removal of misconceptions.