Can I create a web page and write research on it and then publish in an arxiv site or a magazine? Do the laws of magazines allow this?
What a journal will publish is up to them and they have their own rules about pre-prints. To a certain extent this varies by field. Math publishers, for example, are pretty tolerant of author loaded pre-prints to arXiv, but it is less common and accepted in other fields. So, if you have a paper at the "ready" stage, first look at the policies of the journals you might want to publish in to see if they will accept a paper that has appeared in some earlier form.
Some journals will, themselves, put papers on arXiv once the paper has been accepted.
And, avoid predatory publishers, who will publish anything for a fee, usually with minimal verification of the value of the work.
Note that journal publication is to be preferred, since you get a good look at the paper and a vetting by experts along with some advice for improvement. However, it takes time to get published.
Open-access publication is like journal publication, though it has a different way of distributing costs. The authors (rather than readers) pay the costs, which can be quite high. Grant funding of authors can often be used to pay these costs, passing them from authors to the funders - perhaps governments.
Publishing in arXiv and similar doesn't give you that same level of review. They try to keep out complete nonsense, but otherwise, a lot of questionable stuff will appear. You might get some feedback from those who find your article, but it isn't guaranteed to have the same quality as a journal review. It might even be completely bonkers.
Publishing yourself is a waste of time, effort, and money if you have other options. First there is no vetting at all. Anyone can publish anything. Second, it can be very difficult to find your work if it is on some random website. No one can have any faith that what they do find has any validity unless they are willing to do the vetting themselves.
If you are already well known, with a popular web site the above caveat doesn't apply. People will find you and they may already trust you and, so, trust what you write. But for a newcomer, work toward building a reputation through journal publication first and use arXiv, etc., only if permitted and accepted in your field.