Rules & Regulations Of Hogwarts School Of Witchcraft & Wizardary

Question

What do you think would be the requirements in getting admission in Hogwarts School of Witchcraft and Wizardry?

Would a child of 10 years old gain admission if he were to turn 11 in the months to come after July, for example December?

Will his/her relationships with anyone matter, like Draco Malfoy had relations with Death Eaters and other stuff like that?

Answer 1

Would a 10 year old child gain admission if they were to turn eleven in a month after July (e.g. December)?

Hogwarts admission letters are sent to potential students shortly before their eleventh birthday (Harry started receiving letters in the week prior to his actual birthday, if I recall correctly). Given that the school year starts on the 1st of September it seems likely that any student who turned eleven on, or before, the 31st of August would be admitted to Hogwarts for the coming school year. However, if your eleventh birthday was after the 1st of September you'd have to wait until the next school year to gain admittance; for those with birthdays in September and October they'd be approaching their twelfth birthday when they finally started at the school.

There's no canon information to back that up but it reflects the way that school admission works in the UK. Mac Cooper pointed out that there is, in fact, canon information to support this in a FAQ on an old (archived) version of JK Rowling's site:

When Hermione arrived at Hogwarts, was she nearly eleven or nearly twelve? [also asked by vast numbers of people]

She was nearly twelve; you must be at least eleven to attend Hogwarts.
_{JK Rowling Official Site (Wayback machine)}

As for the second half of your question: not in terms of admission. The opinion held by three of the four school founders was that any who wished to learn should be taught, and that's an opinion that was definitely shared by the Headmaster during Harry's time at the school, and I'd assume by most - if not all - of the other Headmasters. Considering that extended to Muggleborn witches and wizards, I can't see any reason that affiliations with suspected, or even proven, Death Eaters would have prevented them from attending the school.

Answer 2

The only requirement for admission is that one be a witch or wizard of the right age.

“No, I am a teacher,” said Dumbledore. “I have come to offer Tom a place at my school.”

“What school’s this, then?”

“It is called Hogwarts,” said Dumbledore.

“And how come you’re interested in Tom?”

“We believe he has qualities we are looking for.”

“You mean he’s won a scholarship? How can he have done? He’s never been entered for one.”

“Well, his name has been down for our school since birth —”

—Harry Potter and the Half-Blood Prince

Recall that Tom Riddle was born in a Muggle orphanage to a very poor mother—not exactly the sort of birth likely to be reported to the Ministry. And indeed, Hogwarts does have an automated way of ensuring admission. The Quill of Acceptance writes the names of all wizarding children in the Book of Admittance upon their birth. From an interview:

In Hogwarts there's a magical quill which detects the birth of a magical child, and writes his or her name down in a large parchment book. Every year Professor McGonagall checks the book, and sends owls to the people who are turning 11.

This also indicates that only those who will turn eleven before the school year are allowed to attend. That subject, however, is sufficiently covered in the other answer.

The approval of the Quill and the Book is the only criterion for acceptance to Hogwarts. As written by Rowling:

In a small locked tower, never visited by any student at Hogwarts, sits an ancient book that has not been touched by human hands since the four founders placed it there on completion of the castle. Beside the book, which is bound in peeling black dragon-hide, stands a small silver inkpot and from this protrudes a long, faded quill. These are the Quill of Acceptance and the Book of Admittance and they constitute the only process by which students are selected for Hogwarts School of Witchcraft and Wizardry.

More specifically, the Book often demands proof of magical talent:

A mere whiff of magic suffices for the Quill. The Book, however, will often snap shut, refusing to be written upon until it receives sufficiently dramatic evidence of magical ability.

This is the only admission test. One's relationship with Death Eaters, the Ministry, or indeed the Headmaster or Headmistress is irrelevant.