Everyone is invited to participate in this contest--unpublished authors, published authors, previous contest winners. Published authors do not necessarily have an advantage here. I've seen brilliant stuff by first time writers and incoherent passages by authors who have several books.
One paragraph only. Multiple paragraphs will be disqualified. If you have two or three very short paragraphs that start your story, you may choose to run them all together and maybe no one will notice.