Is it true that whoever buys honey with the money of his dowry for his wife, and uses it with the intention of healing, will be safe from every disease?

There is no مرفوع hadith concerning this. Rather, these are narrations mawquf (stopped) at Ali ibn Abi Talib, may Allah be pleased with him. Among them is what was narrated by Ibn Abi Shaybah and Ibn Abi Hatim, the summary of which is: that Ali, may Allah be pleased with him, said: "If one of you complains of an ailment, let him ask his wife for some dirhams from her mahr (dowry), buy honey with it, and drink it with rainwater. Thus, Allah combines the wholesome and pleasant, the blessed water, and the cure."