How to use await in a loop

The way you're using the await keyword tells C# that you want to wait each time you pass through the loop, which isn't parallel. You can rewrite your method like this to do what you want, by storing a list of Tasks and then awaiting them all with Task.WhenAll.

public async Task<bool> Init()
{
    var series = Enumerable.Range(1, 5).ToList();
    var tasks = new List<Task<Tuple<int, bool>>>();
    foreach (var i in series)
    {
        Console.WriteLine("Starting Process {0}", i);
        tasks.Add(DoWorkAsync(i));
    }
    foreach (var task in await Task.WhenAll(tasks))
    {
        if (task.Item2)
        {
            Console.WriteLine("Ending Process {0}", task.Item1);
        }
    }
    return true;
}

public async Task<Tuple<int, bool>> DoWorkAsync(int i)
{
    Console.WriteLine("working..{0}", i);
    await Task.Delay(1000);
    return Tuple.Create(i, true);
}

Your code waits for each operation (using await) to finish before starting the next iteration.
Therefore, you don't get any parallelism.

If you want to run an existing asynchronous operation in parallel, you don't need await; you just need to get a collection of Tasks and call Task.WhenAll() to return a task that waits for all of them:

return Task.WhenAll(list.Select(DoWorkAsync));