Images and fonts are important elements of a web page that can affect the cross-browser compatibility for mobile devices. Variations in size, format, quality, and rendering across different browsers and devices can impact loading time, bandwidth, and appearance. To optimize for cross-browser compatibility on mobile devices, you can use image optimization techniques such as reducing file size and format without compromising quality or resolution, using tools such as ImageOptim and TinyPNG. Image responsiveness involves adjusting dimensions and resolution of images to device screen size and orientation; this can be done with srcset and sizes attributes, picture element, or image-set function. Font optimization includes reducing file size and format without compromising readability; tools such as Font Squirrel and Fontello can help compress and convert fonts into formats like WOFF and WOFF2. Font responsiveness involves adjusting size and style of fonts to device screen size and orientation; media queries, viewport units, or rem units can create fluid font sizes with help from tools like TypeScale or Modular Scale.