what did Pope John Paul II do in bringing the fall of Communism in Eastern Europe and Russia?

About as much as Ronald Reagan did.

Nothing at all.

The Russians shot themselves in the foot. They didn't need any help.

Love and blessings Don

He supported the Polish Dock workers on their strike against the Communist Rulers,which accelerated their downfall.

Hello dear!
Well, after the tea Brzezinski had with him (before he became Pope) the history line had changed.
The 14 day Pope died while sleeping and the new Pope managed (being Polish) to start the destruction of Poland and the Soviet Union, ...

he was able to keep the doors open for the freedom of religious expression in the Catholic countries like Poland under Communism.

any sort of freedom (including freedom of religious expression) is deadly for communist regimes.

He stopped the action of the soviet union in Poland. He was a very influential person in Poland. His talks with Jaruzelsky contributed to release the tensions created by the syndicate Solidarity . He prevented the Russian military action against Poland. This created restlessness in the comunist block, whose populations saw the effect of the Pope and realized that the soviet union could be defied