Calling properly TypeScript code from JavaScript

Simply said, if you have to integrate/use a library which is written in Typescript in your own project which uses JavaScript, you will use the compiled JavaScript API!

You basically throw away everything which TypeScript brings in terms of benefit over pure JavaScript.

Meaning you don't have to care about anything specific to TypeScript, like generics etc. You only have to work with the compiled output of the TypeScript library...

To give you an example, go to http://www.typescriptlang.org/Playground Select "Walkthrough: Generics". On the right you should see the compiled JavaScript. It has no generics or anything special, it still is pure JavaScript. That's what you have to deal with...

to your "specific" questions:

• what will be the JavaScript shape of the TypeScript API that extensively uses generics, class hierarchies, interfaces? See above. It will be plain good old Javascript. No difference for you.
• are there any issues with bundling, minification, AMD? No, because compiled TypeScript is plain JavaScript and can be minified etc...
• is it possible to have the basic Angular controller written in TypeScript and the other JavaScript Angular controller that inherits the functionality from it? What will be the caveats? Yes of course you can do whatever you want with the compiled JavaScript.

The only disadvantage of using the compiled JavaScript from Typescirpt is, that you throw away the awesome features TypeScript can give you, like... types... If the other team is already on that route, you may want to consider to write your part in TypeScript as well ;)

The justification that TypeScript is essentially compiled into JavaScript seems to be obscure because there are no trustful sources on information on the topic on how to properly consume that compiled JavaScript from handwritten JavaScript and what are the hidden caveats

Consuming TypeScript from JavaScript is the same as consuming TypeScript from TypeScript, or JavaScript from JavaScript for that matter. For example, let's say you have a function in TypeScript:

function f(n: number) { return 'the number is ' + n; }

To call this function from TypeScript, you would write

var x = f(42);

To call this function from JavaScript, you would write

var x = f(42);

Let's say you have a class in TypeScript:

class MyClass { /* ... */ }

To use this class from TypeScript, you would write

var c = new MyClass();

To use this class from JavaScript, you would write

var c = new MyClass();

In other words, it's exactly the same. No guidance has been given because none is needed.