It is perfectly possible to get married in a Catholic church in Poland as an atheist; I've been to a couple of weddings where one of the happy couple were atheists.
That has nothing whatsoever to do with this case. Nor is it as easy to do as you seem to think, as it requires dispensation from the Bishop, meaning extra hoops to jump through.
Get another priest;
Not an option if she wishes to get married in her home parish.They have to deal with her pastor on his terms. And he has to follow the rules of his bishop. Also, bribes don't always work.
Again, in the somewhat unlikely event that that presents a problem, your choices are either that he lies, or you find a new priest or you make a generous donation to the 'choirboys summer holiday fund'.
It's quite likely, especially in a sacramental marriage between two Catholics, in which the witnesses are supposed to represent the faithful of the Church. Nor will lying do any good. He will probably also have to provide a letter from his pastor, as well.
No, that is not needed. A few priests might insist on such a letter but very few will actually check up on that letter; and the majority of those who do would most probably forget about it if the right donation were to be made to the 'communion wine fund'.
The only thing that matters is what the pastor of the church they will be getting married in requires, and between Catholics, this type of letter is the rule, rather than the exception. Again, bribery does not always work, and might backfire, which means that they will have to find another parish in which to get married, which will require an explanation.
This is her pastor's game and she has no choice but to play by his rules. He is not obligated to marry them if they do not fulfill his requirements.
This isn't some protestant or civil marriage where anything goes.