When should the supplication of Yunus be recited: immediately before supplicating (after praising Allah and sending blessings upon the Prophet), or before praising Allah?

There is no specific time for supplication. It can be initiated with the supplication of Dhul-Nun, "There is no god but You; glory be to You! Indeed, I was of the wrongdoers." Then, one may supplicate for whatever they wish. This remembrance opens the door to supplication and encompasses two types of supplication: the supplication of worship through "There is no god but You; glory be to You!" and the supplication of request through "Indeed, I was of the wrongdoers," which includes seeking forgiveness. The supplication of Dhul-Nun is among the most eloquent remedies for distress, worry, and grief, and the most effective means to Allah for the fulfillment of needs.