Pro se is representing yourself (not having a lawyer represent you in court proceedings).
This is a Latin phrase which means, "the good is to be done and pursued, and evil avoided." It is the first precept of Natural Law, which means that, as St Thomas Aquinas held, it need not be further reduced or explained, because it is self evident to any thinking person.
The write of habeas corpus ad prosequendum is used to transfer a defendant from the jurisdiction where he is held to the jurisdiction where he is going to face charges. It is also used in federal court to arrange for transportation of a witness who is in custody. So someone is arrested in California on a warrant out of Texas. Authorities in Texas file the writ and the defendant is transferred to Texas. Or someone in New York wants to call a witness who is in custody in Florida. The writ is filed and the US Marshals would bring the witness from Florida to New York to testify for trial.
When the person who wrote it dies. All wills have to go through probate, other wise the state isn't sure that the wishes of the deceased were followed. It also insures the taxes are paid and property properly transferred. Consult an attorney in your state for what applies there.