New aliases, double content

What is the problem?

After seo optimization the old latin urls are still listed in google and when i try to open an old link, it opened under the home page, there is no 404 error for no existing page.

That means your sef component works good.

I do not have these urls anymore, the aliases have been changed, and instead of shwoing 404 error, the article opens under the home page. A normal single article doesn`t open this way. On the screenshot I have the home page at the top and the article at the bottom. I don`t want these article to show this way - under the home page.

That is setting in your SEO component probably or in .htaccess file depending how you did SEF optimization.
Who ever did you SEO optimization should know where to turn that off or configure it differently and that is no subject of this forum.

I think that is very weird that something shows under the home page, that`s all.