Every publisher does—if the manuscript is good enough.
It seems to me, that you haven't understood some fundamental concepts in the publishing industry.
It could be a focused publisher or a traditional mega-publisher that has an initiative (a campaign, a sub-division, a satellite company, a focused media channel as in a magazine, a worldwide competition, etc...).
Well, the main focus of a publisher is making money. Every initiative is supporting this goal. If they figure out that it does not make money, they cancel the initiative.
Nothing else whatsoever is really that important.
As found in Version 1 sans edits
Maybe for you. But for the publisher money is important. A publisher has no use for a "I just want to be published" writer. If your manuscript is promising enough to make money, they will take it. Otherwise not.
The contract lets me keep copyright after it's over.
As found in Version 1 sans edits
It's over when it is not longer available in "print". In the age of epublishing this means never. Like everything else, that's negotiable, but you should have someone (like a lawyer) who is good at it. Even then, the odds for an unpublished newcomer are not the best.
Talking about epublishing: Why don't you do it? If you believe in what you write, why do you want to wait for the permission of a publisher? Welcome to the 3rd Millennium; publish it yourself.
Edit: Answering to the edited question
I can't go with self publishing for numerous reasons not the worst of which is the time it would require from me in school times or my financial state.
This still shows a fundamental misconception. I advise you to read the posts here about publishing, self-publishing and query letters.
If you had mentioned your legal state, I may have understood that. Maybe you need the help of your parents to self-publish, because you have not attained full age yet. I don't know something about that. But financial state isn't an issue nowadays, because you do not need (and shouldn't) pay someone upfront to publish your book. That would be vanity publishing. Also look for that keyword.
If you epublish e.g. on Amazon, they take a percentage of every sold book. But you can upload it for free.
Time is always an issue, but if you think you can save time by querying a traditional publisher, I have to disappoint you. Maybe you are lucky and the first one will take your book, but it's unlikely.
So you have to write a lot of query letters. Some editors look first on your manuscript, so the query is not as important, but some look first at the query letter, so that should be better good. And they do not want to read a letter you have written once and send to dozens of publisher. You need time to learn how to write a query letter.
Then you need patience, because it takes weeks or even months till you get an answer, if you get an answer. I don't know what you want to do in your free time during these months, but I have two brilliant suggestions (and they are brilliant, trust me):
- Write your next book
- Learn how to self-publish
And again, because it looks like you still do not understand it: There are no publishers who deal favorably with young writers. There are only publishers who deal favorably with writers who make them money no matter how old these writers are.