So I'm eighteen; I'm a high school student. Say I want to publish something and submit it to a literary magazine (a real literary magazine, not Teenink or whatnot) - will my age/educational status automatically sink me? I don't want advice on whether or not it's wise to submit work at eighteen, merely on whether or not getting published is plausible, assuming that the work is of sufficient quality.
If you submit something of quality that meets their current needs, being 18 and in high school will have little or no impact on their decision.
Age (and the fact that you're a high school student) doesn't matter, and getting published at your age (or younger) is definitely possible.
An eighteen year old can sign, and be held to, a contract, right? If so, then I don't see an issue as long as the work is good. You can sign your own contract, and the magazine won't, as far as I know, worry about whether you'll produce future work, in the way that an agent or book publisher might.
The cover letter need not contain a biography. That can be provided later, after the manuscript is accepted. Stick to the important elements - the request for consideration for publication, and a synopsis of the story.
if what you have to offer is highly marketable, no one will care how old/young you are... nor will they care if you don't include a bio section in your query letter, if it's well written and hooks them on the book...