ASP.NET and async - how it works?

Is this described behaviour right ?

Yes.

Is it correct ?

Yes.

is the DoSomeHeavyWork processed inside task1 or where (where it is "awaited") ? I think this a key question.

From the current code, DoSomeHeavyWork will asynchronously wait for Task.Delay to complete. Yes, this will happen on the same thread allocated by the thread-pool, it won't spin any new threads. But there isn't a guarantee that it will be the same thread, though.

which thread will continue to process the request after await?

Because we're talking about ASP.NET, that will be an arbitrary thread-pool thread, with the HttpContext marshaled onto it. If this was WinForms or WPF app, you'd be hitting the UI thread again right after the await, given that you don't use ConfigureAwait(false).

request produces thread allocating from the thread pool, but response will not be sent until the DoSomeHeavyWorkAsync finished and it doesn't matter in which thread this method executes. In other words, according to single request and single concrete task (DoSomeHeavyWork) there is no benefits of using async. Is it correct ?

In this particular case, you won't see the benefits of async. async shines when you have concurrent requests hitting the server, and alot of them are doing IO bound work. When using async while hitting the database, for example, you gain freeing the thread-pool thread for the amount of time the query executes, allowing the same thread to process more requests in the meanwhile.

But how IO completion thread calls back thread pool thread in this case ?

You have to separate parallelism and concurrency. If you need computation power for doing CPU bound work in parallel, async isn't the tool that will make it happen. On the other hand, if you have lots of concurrent IO bound operations, like hitting a database for CRUD operations, you can benefit from the usage of async by freeing the thread while to IO operation is executing. That's the major key point for async.

The thread-pool has dedicated pool of IO completion threads, as well as worker threads, which you can view by invoking ThreadPool.GetAvailableThreads. When you use IO bound operations, the thread that retrieves the callbacks is usually an IO completion thread, and not a worker thread. They are both have different pools.