My blog does not look the same on the front page like when people click on my home button.
Your "Home" button does link to your front page, so I'm not sure what you mean.
The customer service just told me that it is not possible to have categories on the front page.
I guess you mean that a dynamic category page can not be set as the front page. That's true.
I notice that the "My Blog" menu item of https://mattontour.com links to the "All" category page, the archives page of posts with the category "All" assigned to them. If that is where you intend to display all of your posts, then there's an easier whay to do that. When you assign a static page as your front page, you may assign another page as the posts page at the same place, Customize > Static Front Page. See the Optional -- Create a blog page section of the Set a Static “Home” Page (Front Page) support page.