Is it true that whoever commits zina [unlawful sexual intercourse] in his home will never experience good fortune, will find his money scarce, and his affairs difficult, and is there a solution for that?

Sins negatively affect one's provision (rizq). As for the statement that a house where a sin was committed will not be entered by good fortune, there is no textual evidence regarding it. We advise sincere repentance, for whoever repents, Allah will accept his repentance and facilitate for him the means of provision.