Though literature reviews can be a great way to familiarize yourself with scientific publications and get exposed to scientific writing, they are to be written by "experts" on the topic of the paper. You will sometimes hear lit. reviews referred to as "expert reviews", as they are supposed to critically evaluate a representation of the most important papers written on the subject. Contrary to what some people here will say, they don't necessarily take "months" or "over a year" to write, but they will be extremely time consuming if you don't have an excellent mentor who can guide you through the selection of publications and provide you a basic framework for your paper. It is also best to not have your first paper be a literature review unless you know your research mentor is well-known in the research world in your topic and can almost guarantee that you will be published, or unless the paper is solicited (journal invited your mentor to write the paper).
I would reach out to researchers at MD schools in your area and see if you can hop on a project or help with writing. It is a long shot for DO students, but you can give it a shot. If you have any active researchers at your DO school, that might be easier to get in on, but the rewards will be far lower since they likely won't have any influence in writing letters for when residency comes along.
They do. Producing papers in strong journals with basic science research looks extremely good for residency, especially in research-heavy competitive specialties. But in order to even attempt this, you should already have a lot of experience in basic research prior to medical school, otherwise you will sit around and waste all your time learning things for a long time and end up producing very little or nothing at all. Chart reviews or prospective clinical research studies are easier and will allow you to publish more in the short amount of time you have in medical school to actually do research.
