You seemed to be confused as to what rights are.
"A right is something that is independent of itself. You are living, and therefore, you have the right to continue living until natural death, or until you lose that right for committing an extreme crime."
This is called a natural right. There are more types of rights than this, but I'll get to that later. Natural rights are the shakiest and most debatable when it comes to human rights, because they are based on morality. Morality is always being debated, and has no definite authority figure or set guideline. (Well, there's arguably God, but there is no proof of the existence of any deity, and assuming you live in the United States, neither of us live in a Theocracy.)
It is also arguable whether all humans even have the right to live. You state that humans lose that right when they commit extreme crimes. (You aren't specific here, so I'm going to assume that it only means murder, unless you specify otherwise.) There are also those who say that natural rights are inalienable rights, which means they cannot, under any circumstances, be taken away.Some are against capital punishment, as it is believed to be an infringement upon these very natural rights.
Then there are Legal rights. [link] Legal rights are the rights given to you by your legal system. They are indeed, rights. Examples of this would be the Miranda Rights, which must be read to you when you are arrested, as you also have a right to KNOW your Miranda rights.
Finally, there are civil rights. The people's rights to not be oppressed by their government or private organizations. (Examples of private organizations would be any church.) Examples of these would be the right to self-defense, the right to vote, and the rights to equal opportunity for everyone no matter their race, gender, sexual orientation, gender identity, national origin, color, ethnicity, religion, or disability.
One of your flaws in this topic is that you claim that all rights are "independent of themselves" or in other-words, they cannot be rights if they require somebody else to do any sort of action in your favor. This is not in any legal definition of "Rights", nor is it in your Constitution, which is what all of your legal rights are based on. It's not in the dictionary, either. It does not include legal or civil rights. You have a right to an attorney should you ever be tried. This requires an attorney to defend your case, even if (s)he believes you did wrong and personally doesn't want to defend you. You also have a right to a trial by jury, which requires a number of randomly-selected citizens from your county to stop their lives and pay attention to your trial. These are all legal rights, and they go against your definition of "rights independent of themselves."
And lastly, why you are not correct about abortion being a right. Abortion is a legal and civil right in your country, and is therefore... a right.
It is a legal right because it has been ruled by the Supreme Court that a woman making her own choices about her reproductive system is covered by the 14th Amendment of the American constitution. The Supreme Court and the Constitution are what dictates the legal rights in our country, and while their rulings may change, what is documented as a legal right is considered to be a right while their act is in effect. So right now, abortions are a legal right, and while it is possible, it is not likely to change anytime soon.
Abortions are a civil right because all persons have a civil right to bodily autonomy. Fetuses before the 22nd week are not legally persons, while the woman carrying them is. (Just a note, in government, person=/=human life. There is a push to grand dolphins legal personhood.) It should also be noted that no person has the right to use another person's body against their will. This is why rape, organ theft, and grave robbery are illegal. Intent behind such actions are irreverent, and it makes no difference whether the one doing these things needed to do so to survive. Fetuses before the 22nd week aren't even legally persons, so they have no rights other than natural rights, which are debatable and not enforced.
Just an example of what would happen if the Supreme Court ruled that a person COULD use anothers' body to live, with or without their consent: A dying patient could have you forced to donate a kidney or bone marrow so that (s)he may live.
Anyways, I'm done with the subject matter, I'd also like to critique your essay as a written work. It is unclear if you intended for this to be an informative or an opinion piece. If it's meant to be informative, then I suggest that you do more research before writing your essay, as your understanding of rights (whether natural, legal, or civil) is very shaky. You made the mistake of assuming that rights are a simple, black and white subject, and wrote very little about it except for a vague definition. I even googled your phrase of "Rights being independent of themselves" and there are no sources to back that statement up. It is also good to use sources to back up your claims. (You could put them in a bibliography.) If this is meant to be an opinion piece, then I suggest you write about why you think abortions are immoral rather than what you think rights are, as the definition of rights are based in fact and not opinion. Instead, you should use facts to back up your opinion, rather than trying to rewrite fact as an opinion. Morality, on the other hand, is not so easily defined, so you'd probably have a much easier time getting your point across with an essay like that.