How to scientifically approach theories and research them as a high school student to get it published? (Given that the theory is not yet proven by anyone and may or may not be true).
You will need an experienced researcher to guide you. Most high school students that I know who have published had help from their parents (usually professors), or a professor who is associated with a school. An example is Intel's science competition. Have a look at the students who participate every year, their support system; e.g., mentor(s).
As a high-school student, you are going to have three or four main difficulties, all of which will probably require the assistance of an experienced researcher. The difficulties you will encounter are: (1) finding out what is already known and published about the topic (what we call a "literature review"); (2) knowing the substantive method to use to investigate the topic; (3) if the paper involves data analysis, knowing enough about statistics to do this analysis; and (4) being able to write the resulting paper in an appropriate way for submission to a journal. All of these are hard skills, and they are usually taught over the course of a full undergraduate and then postgraduate research degree at university. It would be hard for a high school student to have skills sufficient in these areas to produce something publishable.
Having said that, if you have a good and novel research idea, and you have a rough idea of how to do the research in a substantive sense, you might be able to find an experienced researcher who is willing to help you (perhaps in exchange for co-authorship or even primary authorship) of the resulting paper. Most high-school students who have published papers in academic journals have had help from researchers who are family friends or parents, and if you don't have these connections it will probably be difficult to get the required help.
I recommend you start by reading some papers in academic journals in the field that contains the topic of interest to you. Browsing some articles in those journals will give you a sense of what is required to produce a published paper. If that doesn't put you off, write up the goal and methodology for your project and show it to some academics in the field to see if it makes sense, and to see if you can find a researcher interested in helping you. Bear in mind that when academic researchers collaborate with students, we are usually dealing with PhD students aged between about 24-40 years old, who already have a strong undergraduate degree in their field. Consequently, convincing a researcher to collaborate with you will require you to show an unusually high level of ability for someone your age.