What is the ruling on saying: "O Lord, if the examination goes well and it is not found that I am afflicted with a serious illness, I will make a portion of my salary a continuous charity for the sake of Allah"? Is it a promise, a vow, or what? And what are the implications?

If, when uttering the phrase "If it does not become clear that I am afflicted, then I will make...", you intended it as a vow (nadhr), then it is considered a vow and you are obligated to fulfill it, according to the hadith: "Whoever vows to obey Allah, let him obey Him." However, if you did not intend it as a vow, then it is not binding, because it falls under the category of ambiguous expressions (alfāẓ al-kināyah). Some jurists are of the opinion that fulfilling it is obligatory. It is commendable for a Muslim to abide by what he has resolved to do, whether it is an action or an act of kindness.