This subreddit has a few very frequently asked questions, so here are some answers.
1. How did it only take 4 years for the Hail Mary to travel 11 lightyears?
Answer: Time Dilation.
The Hail Mary uses very efficient engines to approach the speed of light. At those speeds, time is not constant. On Earth, it took the Hail Mary 13.7 years to travel to Tau Ceti. For Ryland Grace, it only took about 4 years. Don't be an Eridian, learn more about Time Dilation and Special Relativity!
2. Why couldn't they just wait for the Astrophage to double, and then do a return trip?
Answer: It would take longer than 8 days, and they would need more than double the fuel.
a. Whilst small amounts of Astrophage in a lab can double every 8 days, the limit for Project Hail Mary was the amount of energy it takes. Eva Stratt devoted a quarter of the Sahara Desert to be covered in 'Blackpanels', little Astrophage breeding solar panels. This allowed them to make one metric tonne of Astrophage every day.Astrophage os very hungry for energy, and to use Astrophage for fuel, it needs to be 'enriched', or made so that every single cell is full of energy.
b. It would take more than double the fuel. For a return trip on a rocket, the fuel to get back, 2 million kilograms for the Hail Mary, is the payload to get there. The Hail Mary had a 20 to 1 fuel mass ratio, so 2 million kilograms could get 100 thousand kilograms of food, ship and Ryland Grace to Tau Ceti. A return trip would have a payload of at least 2 million kilograms, so they would need another 40 million kilograms of fuel. This would take 20 times as long as it took to make fuel for a suicide mission.
3. Why couldn't they make more Astrophage on the way there?
Answer: Astrophage is really hungry!
To make the 2 million kilograms of Astrophage for a one way trip, they needed a lot of energy. They got this energy from the Sun. During interstellar travel, the Sun, and other stars, would be way too dim to feed Astrophage. The Hail Mary also has a far smaller area to collect any solar power, so it would take many decades, if not centuries to make enough Astrophage. Astrophage also requires physical matter to grow, such as Carbon Dioxide. The Hail Mary couldn't carry all of that CO2 on the way there without a whole lot more fuel.
4. How can Eridians see the Petrova line, and stars?
Answer: Eridian science has come a long way!
While Eridians can't see light themselves, they have developed technology to detect light. They haven't figured it all out yet, as they don't know about Special Relativity and the speed of light, but they can detect light and use radio waves for radar and communications. They used this technology to learn more about their Petrova line, and find out about Tau Ceti.
Eridian scientists likely theorised about their star, because just like on Earth, all of the energy comes from the Sun. The only difference is that Erid's thick atmosphere means that the ecosystem starts all the way up in the clouds, and gradually transfers energy downwards. Eventually, when they built a space elevator, they would have found out a whole lot more about stars and planets. We don't know whether they did this before or after the Astrophage crisis started.
5. How did Eridians not know about space radiation, if they do know about light?
Answer: Space radiation is a bit different!
In Space, especially interstellar space, the most dangerous type of radiation is cosmic rays. These are very fast moving particles, such as protons and electrons, which when they hit Human or Eridian ships at nearly the speed of light, can sometimes pass through the material of the ship, and damage DNA. Eridians don't know about these because their planet's massive magnetic field protected them from all radiation, even when they're on their space elevator. Light is a different type of radiation, and some of it is dangerous, gamma rays, and most of it is not. There is also radiation from radioactive materials, but we don't know if the Eridians have learned about those. So, to summarise, even though the Eridians know about light radiation, they didn't know that space was filled with cosmic rays.
6. Why didn't they collect Astrophage from the Petrova line, at Venus, or at Tau Ceti?
Answer: Space is big!
'You just won't believe how vastly, hugely, mind-bogglingly big it is.' While the Petrova line contains enormous quantities of Astrophage, it is also very, very sparse. The Petrova Taskforce sent a probe to Venus, and could only collect and return 100 cells to Earth. To fuel the Hail Mary requires 2 million kilograms, which would be many, many more cells. The collector would have to be many kilometres in diameter, or wait for many years, to collect enough for a one-way trip. Such a collector would be too large and heavy to send to Tau Ceti.
7. What happens to the other stars near Earth?
Answer: Not much! (credit to u/Equivalent-Board206)
Astrophage, when left completely unchecked, dims a star by a maximum of 10%. That is just barely noticeable to the naked eye, looking up at the night's sky.
Lowered solar output would force the habitable zone (sometimes called the Goldilocks zone) closer to the sun. This may result in previously habitable planets being thrust into glacial ice ages and rendering them entirely uninhabitable. In theory, it could allow previously uninhabitable planets to become habitable, but habitability requires more than just being in the habitable zone.
For Earth, the lowering solar output was leading to a global average temperature drop of about 8°C which would result in rapid glaciation and global agriculture collapse.
Mars too would be colder. Venus has a permanent runaway greenhouse effect and would see no perceptible difference. Nor would the gas giants as they already receive less than 5% of the sunlight that Earth receives.
Beyond impacts to weather and habitability, a drop in solar output would not have any effects on the planets themselves or their orbits.
8. How does Rocky understand Grace?
Answer: Eridians are really smart!
Eridians have extremely good memory, due to the way their brains work. This is especially true for audio memory, because that is the main way in which they interact with the world. At the same time that Grace was recording sounds on his laptops, and writing definitions, Rocky was listening to Grace's words, and remembering them with their respective definitions. They started with charades, but later on they were able to ask each other for definitions of words, and how they are said in English or Eridian.
Disclaimer: Zero AI was used in this post. Not even spell check. (I just added bold text to make it look a bit better).
Note: All redditors that frequent this subreddit, please please rewrite these answer, and I will put them in the post body. Also please add more Q&A, because I can only remember these two FAQ off the top of my head.