How are you downloading the images? If the browser is saying it's saved to Favorites it sounds like it's just bookmarking the image and not actually saving the file...
Once you download an image with a supported format, it should automatically show up in your Gallery (unless, for some reason, the folder where these download is marked with a NOMEDIA file, which basically hides any media in that folder from the Gallery). Even if it was 'hidden' from the Gallery app, you should still be able to find the file with a File Manager app, either by searching for the file name or finding the folder where they're stored at.