using external JS libraries in my angular 2 project

If you use angular-cli, you can add all your external JS files in assets folder. And then in angular-cli.json add them:

"scripts": [
        "../node_modules/jquery/dist/jquery.min.js",
        "../node_modules/bootstrap/dist/js/bootstrap.min.js",
        "../node_modules/moment/moment.js",
        "../node_modules/chart.js/dist/Chart.bundle.min.js",
        "../node_modules/chart.js/dist/Chart.min.js",
        "../node_modules/ng2-datetime/src/vendor/bootstrap-datepicker/bootstrap-datepicker.min.js",
        "./assets/js/slimscroll.min.js",
        "./assets/js/inspinia.js",
        "./assets/js/metisMenu.js",
        "./assets/js/footable.all.min.js"
      ]

You can do it also with external styles:

"styles": [
        "../node_modules/ng2-toastr/bundles/ng2-toastr.min.css",
        "../node_modules/bootstrap-sass/assets/stylesheets/_bootstrap.scss",
        "../node_modules/font-awesome/scss/font-awesome.scss",
        "../node_modules/ng2-datetime/src/vendor/bootstrap-datepicker/bootstrap-datepicker3.min.css",
        "./assets/scss/plugins/footable/footable.core.css",
        "./assets/scss/style.scss"
      ]

And of course you are right, then you need to add in typings.d.ts:

declare var PrayTimes:any;
declare var System: any;
declare var $: any;
declare var moment: any;
declare var Chart: any;

Place all javascript, external css, images etc. in src/assets

(will be compiled to build/assets)

In your index.html: <script src="assets/yourJavascript.js"></script>

Then you can just use it like you describe. (declare var PrayTimes: any;)