I've only read the first chapter, but it seems to underplay the enourmous role the Ptolemaic System and Aristotelian thought had in early modern cosmology, and overplay the role of the Catholic church in preserving geocentrism.
Some historical points to make on the topic which may help as we're reading this:
1. The medieval world thought that the center of the cosmos was corrupted with hell in the middle and the earth around it, whereas the heavens were where God dwelled. They did not think that the heavens revolved around the earth because it was special or perfect. Surrounding to isolate and stop the spread of evil would be closer to their view.
Part of the revulsion towards heliocentrism was because it included the heavenly sun in the earth's ignominy. They felt heliocentrism dragged the heavens down to the earth's level.
Modern writers are not often cognizant of this view and sometimes erroneously ascribe geocentrism to some kind of pro-earth chauvinism.
2. Initially the Catholic church was amenable to heliocentrism. Copernicus dedicated his work on heliocentrism to the current pope at the time.
3. Everyone, including Copernicus and Galileo, wrongly assumed spherical rather than the actual elongated orbits, and though the math didn't work well for either model under that assumption, it worked slightly better for the old geocentric model. Particularly for the movement of the moon which actually does orbit the earth, but also the stars which don't orbit either the earth or the sun.
4. The Catholic church only came down on the side of geocentrism after a series of actual scholarly debates between Galileo and Pope Urban VIII, who were former friends. Pope Leo had written a scholarly treatise and as part of the debate Galileo was supposed to refute it. Instead Galileo created an idiot strawman character called "Simpleton" to represent Pope Urban and parrot his claims which he then argued against. Urban was already worried about assassination and court intrigue so this went over about as well as expected. A trial was convened and Galileo was sentenced to house arrest. He was still allowed to go out as long as he didn't leave the city, and was buried in the Basilica of Santa Croce.
5. To my knowledge no scholar was ever tortured, let alone burned at the stake for advocating Copernican heliocentrism. Just as with modern scientific heretics they usually just lost their funding and their university positions.
6. This was only a problem in Catholic Europe. Protestant Europe embraced heliocentrism, although initially because the Catholics rejected it and screw those guys. Which is why Isaac Newton could freely publish "Philosophiæ Naturalis Principia Mathematica" just 50 years after Galileo's trial, which provided an explanation for Kepler's laws in terms of universal gravitation and what came to be known as Newton's laws of motion.
Edit after more chapters:
A Polish inquisition in the 1400s would have looked at those documents and just gone "Huh, weird, the sun", and wouldn't have even cared. The only people they were interested in hunting for were proto-Protestant Hussites.
Enjoy this manga as great entertainment (because it is) but don't regard the story or its premise as historical or educational.
This isn't entirely true. As you've hopefully finished the manga by now you should see it actually is rather faithful to characteristics of history as we know.
Your first point it detailed out in the second act.
To your second and fifth points you are correct and, in fact, the inquisition itself was a vehicle for the distribution of science and new ideas. Copernicus himself was actually sponsored, in a sense, by the church and died in good standing. The church didnt take a stance against Copernicanism until 1616 which you talk about in your fourth point, but it's worth noting Galileo's work wasnt banned solely because of his poor attitude and tendency to call people sheep. The church had a panel of experts review his work and, partially due to his adherence that Kepler was wrong, which turned out to be false, as well as worries his work was theologically erroneous it was banned. The political motive was certainly there, but the church had reason to believe he was both rude, AND wrong.
Now the educational aspects of the manga are pretty ubiquitous.
1. The ancient greek philosophers and their work mentioned, like aristarchus of samos, heracleides etc are all both real and accurate.
2. The discovery (by Galileo) of the phases of Venus was one of the key pieces of evidence against geocentrism.
3. The church sponsored scientific pursuits.
4. Many of the practices of the inquisition depicted, while theatricized, were also accurate. They did make accused wear monk habits and shackles on trial. They tended to show up unannounced after anonymous tips. They allowed accused to confess in exchange for simply releasing them. They did torture heretics.
This is where most of the inaccuracies also lie. The inquisition didn't torture until a person was convicted of heresy, which was a lot harder than most media make it out to be, and only did so until the 'heretic' agreed to convert. They also never executed anyone. This one is shocking to most people but if the inquisition got to the point of convicting someone as an unrepentant heretic they gave them to the local government to decide what to do with them. Only 2-7% of those resulted in death sentences and usually they just had to bear crosses, go to house arrest or prison, or be exiled.
This is just to say that the story can be regarded as very educational once you see most characters and situations are representations of historical events and not direct depictions of events themselves.