Is it permissible to force oneself to adhere to Islam and perform acts of worship despite deep doubts about the pillars of faith, and is posing this question considered a departure from Islam?

This feeling is a whisper from Satan, and your dislike of it is a sign of the truthfulness of your faith. Turn away from it and do not pay attention to it, for it will not harm you. Allah has overlooked passing thoughts unless they are acted upon or spoken. You will be rewarded for your struggle against these whispers, and the proofs of the Prophet's prophecy, peace and blessings be upon him, are clear.