Just out of curiosity, do the souls in purgatory pray each other out of purgatory?
Or do they just sit there and hope that someone else does pennance and prayer for them?
And if a priest binds that someone is to be released from Purgatory, is God bound by the priest's declaration?
If a priest declares that Hitler's sins are forgiven, is God bound by that one too?
Yes, they could, although this is a commonly held teaching, and not dogmatic. As the poor souls are members of the Body of Christ, one must agree with St. Bellarmine and Suarez that it is possible and permissible to appeal to the poor souls for their intercessions.
And if a priest binds that someone is to be released from Purgatory, is God bound by the priest's declaration?
The priest does not bind anyone to Purgatory. The priest and any other soul remaining on earth can merely beg for the mercy of God for the release of these souls. The Church does not release anyone from Purgatory.
If a priest declares that Hitler's sins are forgiven, is God bound by that one too?
Jesus Christ, having all power and authority from the Father, gave the Apostles the power to forgive or bind sins. If a person makes a valid confession with contrition, that person's sins are forgiven in heaven. The priest serves as the visible means of identifying that one's sins are indeed forgiven. Thus, if Hitler came to a priest with true contrition, God would forgive that monster his sins - just as He promised He would. The ultimate sin is not murdering 6 million Jews, but in thinking that God WILL NOT or CAN NOT forgive a man's sins.
Regards
do the souls in purgatory pray each other out of purgatory?
No, the souls in purgatory lack the free will to pray and so they cannot reduce their stay. We have to do the praying for them.
if a priest binds that someone is to be released from Purgatory, is God bound by the priest's declaration?
Not a priest, but the Pope (who hold the Keys of St. Peter) can define indulgenced work upon which a soul is released. To learn more, see The Enchiridion of Indulgences
If a priest declares that Hitler's sins are forgiven, is God bound by that one too?
If a priest gives an absolution through the sacrament of confession, the absolution binds in heaven, of course. This is the plain meaning of John 20:23. However, a priest cannot absolve a sin that is not confessed in person, and Hitler missed that chance. Had Hitler gone to confession and repented, the confessed sins would have been forgiven him in heaven, and the history of the world would have been different. I hasten to add that if Hitler had confessed but also had continued with his murderous policies, then he would have added an even heavier sin on his soul, as he would have failed to repent.