How can the marriage of the questioner to a girl who used to receive money from young men in exchange for illicit acts be blessed and lawful, and what must be done to purify these funds?

One must immediately repent from falling into forbidden acts and sins that lead to zina (fornication/adultery), such as khalwa (private seclusion with a non-mahram) and gazing [at what is unlawful], and similar acts.

The most important factor that calls for marriage is a woman's commitment to her religion. If she is not committed, then one must seek someone else, unless she repents.

If repentance is realized and you resolve to marry her, then the money taken for an unlawful purpose should not be returned to its original owners. Rather, it should be spent on the general welfare of the Muslims.