Q1: Yes, this is the way that stack works. There is no hover event on mobile devices, so they have to click on the top-level menu (Home in your case) to see the sub-menus. Having the menus work differently on mobile can be confusing. Think of it as just like any main menu in any application. It only shows the submenus. It doesn’t do something on it’s own.
Q2: You can link the logo. It’s very common and users are likely use to it.
I would, however, rethink your layout a bit. Having pages under a “Home” menu is very unusual. Is there a better place for them?