My two cents: [WARNING- long post]
-How much of a composer's future skill is with them when there born (not that they are a skilled composer at the age of 1 week, but that they are going to begin to compose at a very early age and at very high quality).
Well, there's no denying that people are born with different abilities, and there can be a lot of variation even within families. People are born with better and worse ears, more and less creative drives, and so forth, just like people can be born with more or less athletic builds, better and worse color perception, ability to tolerate spicy food, etc. So, of course, some composers were born with a huge amount of innate musical ability and began composing as small children.
However, we can't extrapolate from this that composing is all about innate ability. To drag out a tired example, Mozart was a child prodigy- who was also intensively trained by his somewhat abusive father. Anyone who receives intensive daily musical/compositional training from the age of three is going to be able to write something when he's eight. Of course, Mozart had a high degree of musicality and had the ability to come up with good tunes- I'm not saying he was entirely the product of training. But we can't discount training and family environment when examining the life of anyone, composers included.
Let's take a theoretical example: we have two six-year olds, Garrett and Michael. They are given an aptitude test at school and have identical scores in all areas. Garrett's family has been in the armed forces for as long as anyone can remember, while Michael's parents are writers. So in this artificial scenario, we have two boys with identical musical aptitude, but with radically different home lives.
Garrett has never receieved any musical instruction. He sings in the shower sometimes, and his family will sing along to a CD on a car trip, but they are not especially musical or artistic. Garrett hears a symphony on the radio somewhere and starts listening to classical music. He starts figuring out how to write down his own musical ideas. After a while he asks his parents for violin lessons and shows them his tunes. Though they love him to death, they don't think that music is where a red-blooded American boy belongs, unless maybe he wants to be a rock star and play the electric guitar. His parents, acting purely out of love, tell him that he should play football instead. Garrett is crushed and, in an attempt to please his parents, gives up writing music and goes in to sports. He joins the Marines when he graduates high school and doesn't venture in to composing again until he's honorably discharged at 30.
Michael's musical exposure is initially the same as Garrett's. He hears the same symphony as Garrett and also starts trying to write his own tunes. He asks his parents for violin lessons the same day Garrett asks for his, and shows his parents his works. Being arty types, they sign Michael up for violin lessons and a music theory class. Michael's first quartet is published when he's 16, after ten years of hard work.
This isn't a perfect example, but I think it does a decent job of illustrating my point: aptitude is nothing without the right environment. Also, composing at a young age is not necessarily an indication of early compositional skill. Some prodigies may be able to write music from a very young age but never develop an interesting voice. Some people may be naturally very self-censoring and therefore not develop their compositional interests until a later age, despite a lifelong interest.
So, in conclusion, people are born with certain degrees of aptitude- but aptitude is far from everything.
-How much of a composer's skill comes from just hearing other music and studying music?
This is a weirdly-worded question. There's a big difference between hearing music and studying it.
Composers absorb their musical language from the cultures around them. This is why people who have been raised solely on, say, Indian ragas, will not spontaneously write a Haydn-style string quartet. (Likewise, someone raised on Western classical music will not bust out an Indian raga out of nowhere.) A composer learns about music through listening to it- you music listen to a lot of music to be a good composer. I would venture that the majority of a composer's skill comes from studying music...studying music is how you learn to put your random musical ideas together in to a coherent work. A symphony's theme has to be powerful, but what carries the bulk the emotional effect? The exposition of that theme and everything else a composer does during the course of a symphony. Studying music helps you improve your musical communication. (Of course a symphony's theme is important, but try just listening to the opening theme of any symphony and nothing else. Maybe then my point will be clearer.) Anyone can come up with a tune, but it takes musical training to learn what to do with it.
Sorry, but the wording of this question put me off a bit. It seems a bit like asking how much of a doctor's skill comes from attending medical school.
-Can a person start composing at a very high proficiency level when they're ol without having any previous training or even a thought about music and is there anyone out there who did this?
Can a person start performing brain surgery at a very high proficiency level when they're old, without having any previous training or even a thought about medicine?
Someone who never cared about music, was never interested, never immersed herself in it, is not going to have a modern St. Matthew Passion pop out of her head. Often people who say they haven't had musical training aren't being quite honest. They don't count the years they spent as active members in their church choir, school band, etc. "I fooled around with a guitar when I was a kid, and played in a band in college, but I never really had any musical training," isn't uncommonly heard and, IMHO, completely false. If you played guitar and wrote some songs, you had musical training and you composed. Were you trained by people who had fancy pieces of paper, and given a fancy piece of paper to prove you were trained? No, but you still learned about music.
Proficiency is gained through practice. A child piano prodigy spends several hours a day playing piano. Yes, his brain is wired so that he will learn faster than the average child his age, but it's not like he practices for 20 minutes a day and then goes and plays in the mud like most other kids. Mozart's first works, taken on their own and not as the creative output of a third-grader, aren't anything special. When he was 14, after he'd been working on music for a decade, he was turning out really good stuff. It takes 10,000 hours of concentrated effort to become a master at anything. There are no shortcuts.
My sources are This Is Your Brain on Music by Daniel J Levitin, a few Teaching Company lectures by Robert Greenberg, and a lot of other reading I can't cite.