A favicon.ico is the small icon browsers show in a tab, bookmark, or history list. It's actually a container that bundles a few different pixel sizes into one file. Favicon Generator builds a real one from almost any image, directly in your browser.
Favicons are square. If your source image isn't, it's scaled to fit inside the square and centered, rather than stretched or cropped, so the whole image stays visible.
Yes. A .ico file can bundle several resolutions (16, 32, 48px, and more) in a single file, and some older software and parts of the browser chrome still look specifically for favicon.ico. A single .png only covers one size, which is why browsers increasingly also support PNG favicons declared via a link tag, but .ico remains the most broadly compatible default.
Yes, SVG files are supported directly. They're rendered at each target size before being packed into the .ico and PNG outputs, since .ico and the common icon sizes are raster formats.
No. Every step, decoding the image, rendering each size, and packing the .ico file, happens locally in your browser. Nothing about your image is sent to a server.