Romeo has been hiding in Mantua during the fight between the Capulets and Montagues. The problem is that he is suffering from unrequited love for Rosaline at the beginning of the play.
His name is Mercutio. Mercutio is a friend of Romeo's and a relative of the Prince's. He does not exactly take Romeo's place in a fight: Tybalt wants to have a fight with Romeo but Romeo refuses to fight him. Mercutio, who has been taunting Tybalt right along, thinks it a shame that there is to be no fight and is disappointed in Romeo for refusing to take part, so he challenges Tybalt himself.
The deadly fight between Romeo and Tybalt was not inevitable. It was a result of a series of misunderstandings and impulsiveness on both sides. If they had taken a moment to think rationally or if circumstances had been different, the fight could have been avoided.
Her first assumption is that Romeo has been killed.
No. He was off mourning the loss of Rosaline. He comes after the fray has been ended by the 'Prince'.
The fight in which Tybalt kills Mercutio causes Romeo to kill Tybalt. Because Romeo kills Tybalt he is banished from Verona and is therefore separated from Juliet, who has been placed into an arranged marriage with Paris. The fight is essentially what brings about Juliet's need to fake her own death, which in turn brings about the famously tragic ending.
Romeo initially wanted the fight not to happen, as he had already been wedded to Juliet and did not want to get on Tybalt's bad side, let alone fight him, which would only amplify any hatred between them. However, when Mercutio and Tybalt, both hot-headed and easy to aggravate, started to fight, and Mercutio died under Tybalt's blade, Romeo felt taking his best friend's side as his first priority. He fought with Tybalt out of rage of him killing Mercutio and ended up killing him. simple answer: Mercutio's death by Tybalt spurred Romeo to kill him
The nurse's description of the fight and Tybalt's death leads Juliet to believe that Romeo has been killed. She interprets the news of Tybalt's death as a result of a confrontation with Romeo, and this misunderstanding causes her to despair.
Romeo fights tybalt because while tybalt and mercutio were fighting, tybalt accidentally stabs mercutio under Romeo's arm as he was trying to stop it. Romeo then wanted to get revenge on tybalt for killing mercutio.
Romeo refuses to fight Tybalt when Tybalt challenges him because Romeo is still love stricken after just coming back from his secret wedding to Juliet and is too overjoyed to express anything but love to those that he sees. Not only that, Tybalt is Juliet's kinsmen and I doubt Romeo would want to bring any harm to someone of relation to his only love and now secret wife, Juliet.
Romeo has been acting depressed and waking around aimlessly.
He says that Tybalt came after Romeo but Romeo "spoke him fair", so he then went after Mercutio, and killed him when Romeo was trying to restrain him. He says Tybalt then fled, "but by and by comes back to Romeo" whereupon Romeo killed him, Benvolio being unable to prevent it. This is mostly true, although he withholds the fact that Mercutio went out of his way to start a fight with Tybalt, who had no interest in fighting him. What Tybalt would have done to Romeo had Mercutio not been there is a director's call. The play is clear that in fact Tybalt did seek Romeo out after Mercutio's death, so Romeo was acting in self-defence in fighting him. Tybalt re-enters and Benvolio says "Here comes the furious Tybalt back again." In most movie versions, it is Romeo who chases after Tybalt, which would make this part of Benvolio's account of the fight inaccurate also.
Tybalt was annoyed that he wasn't able to fight Romeo at the Capulet party because Capulet stopped him. He therefore wrote Romeo a letter challenging him to a duel. However since he delivered it to the house and Romeo hadn't been home Romeo never got the letter.