Hello, Brunos,
Thank you for reaching out to us.
1/ Unfortunately, there is no option to upload a different logo image specifically for the mobile menu. However, you can select a static block or template https://gyazo.com/9e4ec1be55fb7b79a51012634fc3f05e that includes your desired image with a link to the homepage.
2/ Theme Options > Styling > Input > border-radius
OR
Custom CSS code can be used: https://prnt.sc/9n4G8b7D6qd8
selector .etheme-search-input-form-wrapper {
border-radius: 100px !important;
}
We hope this information is helpful.
Best Regards,
8Theme’s Team