In the favicon generator result page, there should be a tab for Blogger, which explains how to install the favicon in Blogger.
Apparently, Bloggger expects XHTML (with self-closing markups), not HTML5.
It is not clear if it is possible to get the URL of images in advance (once uploaded, images have non-deterministic URLs). Therefore, maybe it is not possible to offer a simple procedure for blogger.
As a fellow blogger, this is what I did. Since, from what I can tell, Blogger doesn't let you host files on their site, with the exception of the favicon, I opened a Google Site and used it just for hosting the images. Make a page with a "filing cabinet" (as Google Sites calls it) and it will let you host files. Just extract your folder there and copy the download links without all the appended stuff. If you'd like me to clarify anything specifically, just let me know!