Is it permissible for a divorced woman to marry herself in the presence of witnesses without a guardian (wali amr) and without an official divorce certificate, knowing that this is her third divorce and that she seeks to live chastely in a lawful manner?

The majority of scholars stipulate the guardian (wali) for marriage, so your marriage is invalid according to them unless a judge officiates it, basing it on the madhhab of Abu Hanifa. If your first husband divorced you three times, you do not become lawful for him until you marry someone else in a valid marriage, he consummates it with you, and then he divorces you. The absence of a divorce document does not prevent its occurrence.