You can use FontAwesome on GMBinder, pretty easily. I’ve done this on a couple of pages, but I can’t get to the links to share. I don’t think game-icons.net works the same way, unfortunately.
GM Binder is wicked easy to use. You don't need to have any knowledge in CSS or HTML or anything (though anything that you do learn in that area will only help you).
There are preset themes that you can use out-of-the-box, and the default theme is the same as 5e's PHB. There are other themes that you can choose from if you want; just select the one you like best from the dropdown!
Your content will be annotated using Markdown, which you can wrap your brain around after reading this.
all the images might not be optimized for web, so they are all in high quality for printing. They borders, background, and any extra flair all have images associated with them.
You have two options. Take the images and rehost them and repoint the paths to the new host point.
Otherwise, if that sounds daunting you can always use something like smallpdf and compress the pdf after you download it.