How do i create a new custom page

I want to create a new custom page template to use as the homepage.
I just want to take the existing “Full Width” template and only remove the title being displayed. How do I do that?
Also I want to change the default width from 1038px to 1020px. In short, I want the theme to display on a 1024px screen without the sidebar moving below the main content as it happens on a tablet or mobile screen. I want the sidebar to shift down only if the screen is less then 1000px.