Luckily, I go to a school that does not turn down students with disabilities, and I have gotten to know them well enough to sympathize with their quotidian distress and witness their unwavering courage
^Grammatically, 'them' can refer to disabilities, which I understand is incorrect, given the point you are trying to make.
In fact, most of them are quite loquacious despite their speech impediments, and they love to share their weekends with anyone who cares enough not to overlook them
^How can someone be loquacious, if they have a speech impediment. This is a juxtaposition that just does not work.
I do not understand the weekend point you are making. How do people share weekends, and what is overlooked? Weekends? The conversations about weekends??
Nothing stands in the way between them and the world - except for, well, a frameshift mutation in a strand of DNA or nondisjunction of a set of chromosomes during meiosis.
^Are you referring to the weekends here? (Obviously not, but grammatically, you are being ambigious) Also, the informal approach here can be considered insensitive.
The Krieger School of Arts and Science offers not only a large selection of biological courses, but also a wide spectrum of genetics courses that will deepen my understanding of gene regulation and chromatin transcription.
^You may want to state, why you would like to deepen your understanding?
You do make a number of grammar errors in your essay. These need to be rectified.
In terms of content, your essay seems to be on the right page. However, you do not quite provide a strong enough link with the disabled people in your school, and your interest in genetics. As the link is not strong, it is questionable as to whether the first paragraph is even relevant to the essay prompt or what you are trying to say.