I barely remember being six, much less writing letters. Here is the passage.
Writing to his (Edwards) stepmother, the six year old urged her to keep a careful eye on the princess: "preserve her, therefore, I pray you, my dear sister Mary" , from all the "wiles and enchantments of the evil one" and "beseech her to attend no longer to foreign dances and merriments which do not become a most Christian princess." At the same time he praised Mary, telling her, "I like you even as a brother ought to like a very dear sister, who hath within herself all the embellishments of virtue and honourable station."
I could barely spell my name at this age, so what's up?
Given that Mary Tudor's mother is Catherine of Aragon, if their childhood was arranged in any similar fashion to that of children in Spanish Habsburg royalty, then it's almost surely a letter written with significant help by her tutors.
Up to age 6-7, they grew up in the care of especially chosen women, mostly chosen due to their piety and virtue. After this point, they would be assigned tutors, either in male pursuits if they are a boy, or in female pursuits if they are a girl. For boys, this is where they start to be moved into the public domain and take part in royal activities more fully.
So for Edward, he probably had two tutors at minimum. One specialized in scholarly pursuits (in Castile, the maestro) and the other in martial pursuits (in Castile, the ayo). He may already have his own separate household, led by a specially chosen person, who would be on Edward's side effectively at all times. He would sleep in Edward's chamber.
All this, and much more, can be read from G. Parker's "Imprudent King: A New Life of Philip II," ISBN-13: 978-0300196535, 2014.
Probably a scribe. Wealthy men had secretaries (who were also men, unlike today, when "secretary" stereotypically means a woman) who wrote for them. These were men who were skilled at handwriting and would write in a very elegant hand. There were also ways of writing that secretaries used that were specialized and difficult to read. Check out this Elizabethan manuscript: http://latindiscussion.com/forum/latin/translation-of-elizabethan-latin-manuscript.17017/
It's in Latin but even so, hard to figure out which letters are being used, despite being the same alphabet. You can see how it was specialized a lot of time was devoted to the calligraphy. At the time, also, it was common for gentlemen to write in a very messy hand. Since handwriting was considered to be the job of a secretary, it was a hallmark of a gentlemen to be too busy and important to devote time to this kind of menial task, so a gentleman would write messily. So while Edward, the future king, would have been receiving education from a very young age, and he might have been able to read and write despite his young age, he probably wouldn't have been writing the entirety of his own letter to his sister.