The solution is to define your public path in laravel mix, because xampp use another root-path then php artisan serve.
http://localhost/myproject/public/index.php     //xampp
http://127.0.0.1:8000/index.php                 //serve
1 install fontawesome: 
npm i @fortawesome/fontawesome-free
2 Add to your /resources/sass/app.scss:
$fa-font-path:  "webfonts/" !default;
@import "~@fortawesome/fontawesome-free/scss/fontawesome";
@import "~@fortawesome/fontawesome-free/scss/regular";
@import "~@fortawesome/fontawesome-free/scss/solid";
@import "~@fortawesome/fontawesome-free/scss/brands";
3 Add to your header:
<!-- Styles -->
<link href="{{ asset('css/app.css') }}" rel="stylesheet">
4 Add to your webpack.mix.js in your root folder:
mix.setPublicPath('public');
mix.setResourceRoot('../');
5 Add some icons into your blade-files, f.E.
<i class="fas fa-user"></i>
6. Run: 
npm run dev