Hi,

01. To do this, you can use Elementor’s built-in feature called “Responsive Background Image”. Here are the steps to follow:

Add a section to your page in Elementor and click on the section’s settings (gear icon).
Click on the “Style” tab in the section settings.
Click on the “Background” option, and select “Responsive” from the drop-down menu.
Upload your desktop image by clicking on the desktop icon next to the “Background Image” field.
Click on the mobile icon next to the “Background Image” field to upload your mobile image.
Adjust the image settings for each device as needed, such as position, size, and repeat.

02. There is no option in the extra menu list but you can use the product categories widget in the desired location.
Screenshot for clarification:
https://ibb.co/yVRCzWJ

Best Regards.