Does not bringing to mind the intention of drawing closer to Allah affect the validity of the deed or only its reward, and is the ghusl of one who intended to embrace Islam or remove major ritual impurity valid if they were unmindful of the intention of drawing closer to Allah?

The summary of the answer:

Correcting and recalling the intention at the beginning of an action is very important for the acceptance of the action and the rectitude of the heart, for deeds are by intentions. Intention in Islamic terminology has two meanings: The first is distinguishing acts of worship from one another or from customs. This is what jurists mention, and the validity of an action depends on it. The second meaning is distinguishing the purpose of the action, whether it is for Allah alone or for others. This is what the people of sincerity are concerned with, and on it depends the acceptance of the action and its reward. The intention required to correct an action is usually present in the servant's heart without the need to utter it or recall a specific wording, for the purpose of doing something is its intention.