Is it a condition when supplicating to say: "and I am in good health" or "without harm" after every supplication, out of fear that the supplication might be answered with an undesirable outcome, and is what was narrated from Imam Ahmad ibn Hanbal in this regard authentic?

A believer should supplicate using the established supplications from the Quran and Sunnah, due to the goodness and blessings they contain.

As for appending and qualifying a supplication, it should be resorted to when supplicating for something whose benefit is unknown, such as supplicating for death or a long life, or when asking for needs whose benefit might only be realized by qualifying them. This is what happened with Imam Ahmad when he supplicated for memorizing the Quran without qualifying it with well-being, and he memorized it in prison.

So, if a servant asks his Lord for a need, it is better for him to say: "in well-being," unless its benefit is already realized.

Nevertheless, this etiquette should not lead to obsessive doubts (waswasah) or mistrust in Allah. There is leniency in the matter, and one may supplicate for what they believe to be good without qualification.