No, saddly not.
There were some hints to Arya's affection towards Eragon in the third book, her embracing him and running to find him after he rescusing Horst, however it seems that she fears what she feels, and rejects Eragon, who is in love with her. Yet, there is still a chance that the two will grow closer.
Arya- the Elf Princess he meets in Eragon Book
No technically they don't ,you see in book 4 arya finally says she'll get together with eragon but eragon has to leave and i guess you can imagine the drama so unfortunately eragon and arya never get together
the book three of eragon states that arya and eragon do encounter each other they show no romance
In the series, Arya and Eragon do get drunk together after she broke her wrist and caused massive damage to her arm.
Five integral characters in Eragon are Eragon, Saphira, Brom, Murtagh, and Arya. Eragon and Saphira are doubtlessly the most important characters out of them.
Yes Brom dies at the beginning of the 1st book by the razak and then eragon finds arya later
duhhh! read the book its Murtag son of Morzan and Arya the elf (although she was is a coma on the way to the Varden)
Brom said the line "May your sword stay sharp" in the book Eragon.
Durza and Arya are in the Eragon/Eldest/Brisingr trilogy be Chris Paolini, they have nothing to do with Chris Wooding.
roran will be the new king, arya will be the new rider.
They're not as of Brisingr, but they might still be cause Christopher Paolini has announced that there will be 4th book.