Since no one has been able to answer my question, I've taken the liberty to do a little internet research on the subject and answer the question myself. If anyone disagrees, feel free to say so
According to Urban Dictionary, "RP" is a type of writing which usually happens between two or more people. Emphasis on the word "usually." It's not "always." You can write with yourself, or your own non-player character nations, and it will still be "RP," because that is what role-playing is: to assume the roles of your fictional characters and write stories.
I visited another website, and they said that RP "stands for roleplay", "which is where you take on the persona of a character and act as them through a plot. This plot can be put together by you and others or from a show, book, or story you enjoy."
They did not say that you must write with two or more people, or your writing/work would not be counted as a "role-play," which according to Merriam-Webster means "to act out the role of, or to represent in action", your fictional characters (or in this case, your nation's canon and all the fictional characters there)
But what is "stand-alone story"?
I visited Jude Deveraux's website - the real life author of forty-three New York Times bestsellers - and from looking at her website's "Standalone Stories" section, I came to know that "stand-alone story" is just that -- a story (e.g. books, movies) written within the writer's in-character universe, but which doesn't require me to read other stories (books, movies, etc.) within the series for me to understand the storyline. I wrote some keywords on Google Search, and it brought me to the following Quora page: What is the meaning of "stand-alone books"?
Mercedes R. Lackey, 134 industry published books, NYT #1 Bestselling Author, said that It is a book that either is not part of a series, or if it is part of a series, can be read, understood, and enjoyed without having to read any other books in the series. The answers of other people - mostly real life professionals and writers - also seemed to support my conclusion.
From this, I've concluded that the best way to ask should be - A m e n r i a, will you be writing with other people, or make the thread a [closed] thread?
"Are you planning this to be a RP or a stand-alone story?" is a bad way of asking a question, especially when many new players are watching this thread looking up to you (because they know you have the bolded green Mentor badge), because it insinuates (suggests or hints) that a thread where you're writing with yourself or your own non-playable character nations is not a proper "NS RP" or "II RP" thread, [ Edit: and by doing so you're not being a proper NS or II RPer ]
That said, this is my own little research on the subject, and so I'm not an expert here. [ Edit: And if anyone is wondering, I very much respect Sunset as a writer. But I feel I must point that out there for new players and even some older [mostly inactive] players. Once again, anyone feel free to disagree (and I'll honestly be OK with that)
I'm sorry Yohannes, but my Edit: