desktop v mobile menu

Greetings,
Being as the header image in this theme is not responsive, i think i have a work-around for mobile users.. I want to redirect mobile users to https://talhamhomerepairs.com/site/home, but the “home” menu item brings mobile users back to https://talhamhomerepairs.com/site/ which is the incorrect page for mobile..is there a way to change this, while keeping the desktop version home link as it is??

Also how can I disable the link to the index.php file in the site title in the header?

Any insight greatly appreciated..

The page I need help with: [log in to see the link]