Harry and Hermione, along with Neville and Draco, were given detention from Professor McGonagall for being out of bed at night. Harry and Hermione had been giving Norbert to Charlie Weasley at the top of the tallest tower. They forgot to collect the invisibility cloak and were caught by Filch, who had been tipped off to their whereabouts by Draco.
Draco knew where they'd be after he went to the hospital wing on the pretence of borrowing a book from Ron who had been bitten by Norbert. Draco actually wanted to torment Ron and pretend he was going to tell on him. Ron had to give him a book, unfortunately he picked the one containing his brothers letter that gave Draco all the information he needed.
Neville overheard Draco saying he was going to get Harry in trouble and was caught trying to warn Harry about this.
In the movie, this was changed. Neville wasn't involved and Ron was.
Their detention was to go into the Forbidden Forest to find the injured unicorn.
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In the third book, Hagrid becomes Care of Magical Creatures professor and in one of his first lessons, he shows Harry's class (which includes Draco Malfoy) hippogriffs! Hagrid talks to the class about Hippogriffs and how they get easily offended. Draco and his mates are talking during this and don't pay attention. When the class separates into small groups to each Hippogriff Malfoy calls the Hippogriff an "ugly, great brute". Naturally, the Hippogriff, Buckbeak, retaliates and attacks Malfoy, breaking his arm. Therefore, Hagrid takes Malfoy up to the castle to the hospital wing.
He got a detention for being out late, so did Hermione and Ron but they were split up and Harry got stuck with Draco.
This is a very broad question, and not worded correctly. Severus Snape killed Albus Dumbledore in the end of the sixth book. Dumbledore had asked Snape to kill him, to save Draco Malfoy's soul because of the Unbreakable Vow that Narcissa Malfoy made Snape take in the beginning of the sixth book since Voldemort had ordered Draco to kill Dumbledore.
Draco was the actual master of the elder wand because Dumbledore's death was already planned, so when Snape killed him, it wasn't actually a takeover of the wand. Because Draco was the last to disarm Dumbledore, or 'take' his wand, it recognized Draco as it's master. This is how Voldemort was ultimately killed, because Harry was using Draco's original wand. The elder wand recognized the wand as its master's, so Voldemort's killing curse was turned back upon him. However, Draco never actually had the Elder Wand in his possession. He never even knew he was the master until Harry revealed it.
They wanted to find out what Draco was up to. However, Hermione was not subtle enough, and the shop owner, suspecting something, made her leave the shop.
The main characters in the first six Harry Potter books are Harry Potter, Ron Weasley, Hermione Granger, the Weasley family, the Dursleys, Draco Malfoy, Crabbe, Goyle, Albus Dumbledore, Professor McGonagall, Hagrid, Neville Longbottom, Luna Lovegood, Severus Snape, Peter Pettigrew, Voldemort, Mad-Eye Moody, Remus Lupin, Sirius Black, Cornelius Fudge and Dobby. There are a wealth of other characters but these are the ones that occur most frequently.
It is a hospital where the surgery to take out Grusha's eyes happens.