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How compatible is a double major between philosophy and one of the natural sciences?

I think that a double philosophy/science major is a terrific idea (disclosure, I did something like that myself as an undergraduate). It lets you enjoy philosophy without giving up science, keeping your options open for when you graduate. Whether or not (and how) you can do it will depend on your institution.

To what extent is one responsible for how accomplished one can be in life? Many assume that hard work is all that is needed. Personally i'm in college, and i've been getting A's because of hard work. I am however almost tormented by the thought that alot of my childhood was spent doing pretty much nothing. John Stuart Mill was fluent in Latin and Greek by the time he was twelve or so, because he was pushed so hard by his father. Mill was an accomplished man off course, and most people could not do the same things as he did even if they worked hard later in life. Should one just give up trying to excel academically if one has not had a privileged childhood as he did?

John Stuart Mill was a childhood prodigy, as you say, but in later adolescence he suffered a "nervous breakdown" (probably depression) which he thought was caused by too much intellectual work as a child. So, at the same age you are now, he was not very functional. He also died when he was 67--not a long life by today's measures. There are many routes to academic accomplishments; perhaps hard work is the only thing they have in common, and you know that you are capable of that. In any case, you cannot change the past or guarantee the future--only work with the present. If you enjoy academics and aspire to greatness, I wish you the best of luck!

Why do parents have the right to decide anything about a child's upbringing, or their moral, social, political and spiritual education? Young children are trusting when it comes to their parents, and may even believe falsehoods if their parents are the ones who are repeating these falsehoods. So why do we recognize a unilateral right for parents to teach their children whatever they want, and to withhold whatever information from their children that they deem appropriate? Why do we let parents pull their children out of sex ed class, or teach them a religion as a unilateral source of truth? Shouldn't parents have responsabilities, instead of rights? Surely shaping a child's mind, personality and outlook is not the "reward" parents get for feeding and clothing them! Is this just a practical issue ("There's nobody in a better position to take care of the kids, and there's no way we can stop people from teaching them whatever they want")? Or is there some fundamental moral reason parents have the...

I think you are right to claim that parents have responsibilities towards their children, and do not have the right to raise them "any way they want." Children are not property. The larger moral concern, however, is that the state will decide what children are to learn, and in American society, we are most fearful of that (because of our history with totalitarianism and communism). The law protects the rights of individuals. So parents have a legal right to withdraw their children from state-sponsered education. They also have a legal right to teach them rubbish. However, I would argue that they do not have a moral right to teach them rubbish, particularly if it is rubbish that is harmful (Santa Claus probably does not fall into that category; but Abstinence is harmful rubbish).