Help with Site Title Logo and different images on desktop/mobile versions

Site URL: https://werkit.se

Hello,

I am on a "Personal" plan and am looking for help on the following things:

• Removing the site title logo from only the first main page.
• Make the mobile version show a different image on main page and in headers then the desktop version.  

Thanks in advance!

Q1. Add to Design > Custom CSS

body.homepage a#site-title {
    display: none;
}

Q2. You mean site title logo or banner image under header?