Alot of rumors that the last of the dragon eggs will hatch for either the varden or the empire and that it will be a green dragon who will take the sword tamerlein for his/herself
roran will be the new king, arya will be the new rider.
If by main conflict, you mean battle, then it is when Eragon fights a new rider that serves Galbatorix.
he heard it from the townspeople or rumors about a new rider.
The second Inheritance book is called "Eldest" because it focuses on Eragon's training and growth as a dragon rider, making him the oldest and most experienced rider among the new generation. The title also refers to Eragon's internal struggles with his identity and destiny, as he grapples with the responsibilities placed upon him.
There is Eragon, Eldest, Brisingr, and at the end of Brisingr Christopher Paolini writes that the series will conclude with a fourth book. Supposedly there won't be a new trilogy but authors sometimes go back on their word.
Yes, the young girl with arms like a swordsman, Nasuada, will not become the new dragon rider as her mother was. Instead, it is Eragon's unborn child, also known as the Green Dragon Rider, who will inherit this role in the future, as revealed by Angela's bone casting.
I think it will be either Arya or Roran who will become new Dragon Rider in the Inheritance series, although, i hope it is Roran, he would be more powerful than Eragon as a rider, however, maybe not at magic.
In the book Eragon, the conflict was resolved through a final battle between Eragon and Galbatorix, the main antagonist. Eragon was ultimately able to defeat Galbatorix by using cunning strategy and exploiting a vulnerability. After Galbatorix's defeat, peace was restored to the land and Eragon played a key role in rebuilding and establishing a new order.
Christopher Paolini has said he came up with the name by replacing the first letter of the word dragon. Some people feel he lifted the name from Anne McCaffery. In Anne McCaffery's series there was a character named Erragon (with two r's). She has been writing about dragon riders in her Pern series since the 1960's. Paolini has sited these works as a major influence. In the Paolini series, Eragon was also the name of the first ever dragon rider. While I agree with the first two writers information, here is a little more backstory on Eragons name. He was the first dragon rider with a white dragon. But I believe he is still alive. Take all the facts into consideration. There is yet to be another dragon and rider discovered in the final book, but from what the first three, mainly the first book "Eragon" tells us, is that if Eragon ever finds himself in need of advice, go to this place where he can speak his name and I believe there is where he will find the first Eragon and his dragon waiting for him. This new dragon rider coming in the fourth book can be seen swaying from either side. Galbatorix already has Murtagh and Thorn, but from Brisingr, Eragon told him that their true names can change. So Murtagh may finally be rid of his vows to the king. If that were to happen, Murtagh would then definatly switch sides and provide the varden with information on how to bring Galbatorix down. This new rider though is still in the clutches of the king because the egg is still there with him. When that egg hatches to its new rider, you know Galbatorix will make the rider swear oathes to him, like Murtagh, but the rider won't know the information about how his/her true name may change. If the varden can pull off another steal with this egg like they did with Saphira's egg, then the rider will have a chance. In my personal opinion, I think the new rider will be Arya.
In Brisingr Eragon didn't change that much, he learned a few new things, such as the facts about why Galbatorix and Murtagh were so strong. I think Eragon became more mature, he married Roran and Katrina and he has to think of a punishment for Sloan. He doesn't change as much as people around him change. Eragon has to face many hard decisions and he begins to realize the importance of being a rider.
Brisingr is the name of Eragon's new sword, the main problem in the end of book three was that Eragon couldn't fight Murtagh without a sword, connection maybe? If you are talking about other than that, Eragon has to finish his trainig with Oromis in order to be as strong as Murtagh, or so he thinks. The main idea is that Eragon has a lot of things he needs to do before he is ready to face Murtagh.
Well Murtagh thinks Eragon is his little brother.Murtagh is the son of Morzan and so gets his sword. Eragon gets a new sword in the 3rd book.