How can I add a second Menu

Hi there, it is not possible by theme settings. You should use the child and manage the header/template-parts masthead template file

Could you explain a little more detailed how I could do it?

Also, today I noticed that the blog page is not responsive on mobile.

How can I customize the posts page?

Hi, about the blog add this css code into the CSS additional section

@media (max-width: 600px) {
body.blog .blog-posts.columns-2  {
  display: block;
}
}

About the second menu, you should create a child theme and manage the theme template file for the header part that is yith-proteo/template-parts/header/masthead.php and do your coding to show a second menu in there