The problem may be that your site uses a paginate gem that is version 2
But what is allowed on GitHub Pages is only version 1
Also, I can see you followed the instructions in theme, but the instructions mean you end up with something hard to work with. Currently you have the entire theme and your content mixed into one which makes your site unwieldly to work with as it has code you didn’t write and it is hard to change or upgrade the theme.
Your logo question is better as a separate forum topic. But anyway, here goes.
Do you mean the GitHub and Medium icons?
I did a search for “medium” in your repo and arrived here
For example you can change fa-github to fa-twitter and you will see the Twitter logo.
That uses FontAwesome 4 icons - these are loaded because you have this CSS line
You can find more available icons here.
Note that Font Awesome 5 has been around a long time and uses fab instead fa, so you are going to have to either dig to find something that works in font awesome 4, or you have to upgrade your version to 5.