Am i correct that async/await itself has nothing to do with concurrency/parallelism and is nothing more than CPS implementation?
Well, async / await is a rewriting that uses CPS, so your core understanding is correct.
Regarding "concurrency" and "parallelism", I would say that it does enable concurrency; you can start multiple async operations which are all "in flight" at the same time. This is easy to do with Task.WhenAll and Task.WhenAny.
Also, even though async by itself doesn't imply "multithreading", Task.Run does enable easy async-compatible multithreading
And the real threading is performed by SynchronizationContext instance that await passes/restores?
Think of it this way: the continuation created by the CPS rewriting has to run somewhere. The captured "async context" can be used to schedule the continuation.
Side note: the captured context is actually SynchronizationContext.Current unless it is null, in which case the captured context is TaskScheduler.Current.
Another important note: the capturing and restoring of the context is actually up to the "awaiter" object. So, by default, if you await a Task (or any other built-in awaitable), the context will be captured and restored. But if you await the result of ConfigureAwait(false), then the context is not captured. Similarly, if you await your own custom awaitable, it won't capture the context (unless you program it to).
However, are there any guaranties that the thread's context information is persisted? I mean Name, CurrentPrincipal, CurrentCulture, CurrentUICulture, etc.
SynchronizationContext is different than ExecutionContext. A simplified answer is that ExecutionContext always "flows", so CurrentPrincipal flows (if it didn't, it could be a security issue, which is why APIs that don't flow ExecutionContext always end in Unsafe).
In UI apps, culture doesn't flow, but by default it's the same for all threads anyway. Name is definitely not going to flow, unless you resume on the same thread (e.g., using a UI SynchronizationContext).
For some further reading, I recommend starting with my own async / await tutorial and then the official async / await FAQ. Then take a look at Stephen Toub's blog post on ExecutionContext vs. SynchronizationContext.
You may also find my SynchronizationContext article helpful.
