Broadly? Of course. But there are some details which are inaccurate:

King of Poland never granted Rome the power to appoint bishops

It's debatable. Poland has split into small duchies in 11th century, and thus Bishops were appointed by Rome or the Holy Roman Empire.

Readers might be confused when the writer says that Lithuania is three times bigger than Poland, since modern Lithuania is a small country

It's worth remembering that the vast majority of people living in Lithuania identified as "Rusin", or East Slavs.

the forces of the Union were to win every battle they fought for more than a century,

That's probably debatable - if they did, they'd conquer the Teutonic state.

Communism during the 1800s and early 1900s was one of the world great religions

Yeah, color me mistrusted.

Nowadays, schoolchildren in Poland are taught that the szlachta are the selfish villans of Polish history. (...) Because earlier, the szlachta were also heroes of freedom, for two hundred years, starting in the late 1300s. I think a good analogy for the szlachta would be the Republicans in the USA

There's some ideology here, doubtlessly. It's still worth remembering that the Polish nobles were still slave-owners.