System.Threading.Timer vs System.Threading.Thread.Sleep resolution - .NET Timer not using system clock resolution

Question 1

Why is the System.Threading.Timer keeping the 15ms resolution despite the OS clock resolution is much more precise?

Obviously due to implementation. System.Threading.Timer (and therefore Task.Delay) uses .NET runtime timer queue, that not respects system timer resolution. Furthermore, I ran tests (.net 4.x) windows (7, 10; server 2012, 2016) and found, that WaitHandle.WaitOne() and Monitor.Wait() doesn't respect system timer resolution on WinForms GUI thread too (it's for answer above to use WaitHandle). So, only Thread.Sleep respect it on GUI thread.

What is the recommendable way to achieve 1ms timing events resolution without busy CPU waiting?

One way pointed out by Jim Mischel. But, it have drawbacks like:
Callback executing on windows thread pool thread.
Time interval is relative to the current time.
Time interval is integer ms, so theoretically max precision is 1 ms.
By many reports, 1.5-2 ms precision is practically maximum that you can achieve and only with timeBeginPeriod(1) call.

Another approach is: NtSetTimerResolution and Waitable Timer Objects. You may obtain 0.5 ms resolution (depends on hardware and windows version).
For c# example (It's not the example of your timer class, but example of using this functions in c#), you can check this article.

You also can try Nick's suggestion but need to keep in mind problems with GUI thread.

Question 2

Use one of the synchronisation classes that derives from WaitHandle, such as AutoResetEvent or ManualResetEvent, setting the timeout parameter when you call the WaitOne() method.

By calling WaitOne in a loop, you can implement a timer.

You can signal the wait handle derived class to break out of or interrupt the timer.

Note, to change the resolution, you are best off using a helper class that implements IDisposable:

internal sealed class TimePeriod : IDisposable
{
    private const string WINMM = "winmm.dll";

    private static TIMECAPS timeCapabilities;

    private static int inTimePeriod;

    private readonly int period;

    private int disposed;

    [DllImport(WINMM, ExactSpelling = true)]
    private static extern int timeGetDevCaps(ref TIMECAPS ptc, int cbtc);

    [DllImport(WINMM, ExactSpelling = true)]
    private static extern int timeBeginPeriod(int uPeriod);

    [DllImport(WINMM, ExactSpelling = true)]
    private static extern int timeEndPeriod(int uPeriod);

    static TimePeriod()
    {
        int result = timeGetDevCaps(ref timeCapabilities, Marshal.SizeOf(typeof(TIMECAPS)));
        if (result != 0)
        {
            throw new InvalidOperationException("The request to get time capabilities was not completed because an unexpected error with code " + result + " occured.");
        }
    }

    internal TimePeriod(int period)
    {
        if (Interlocked.Increment(ref inTimePeriod) != 1)
        {
            Interlocked.Decrement(ref inTimePeriod);
            throw new NotSupportedException("The process is already within a time period. Nested time periods are not supported.");
        }

        if (period < timeCapabilities.wPeriodMin || period > timeCapabilities.wPeriodMax)
        {
            throw new ArgumentOutOfRangeException("period", "The request to begin a time period was not completed because the resolution specified is out of range.");
        }

        int result = timeBeginPeriod(period);
        if (result != 0)
        {
            throw new InvalidOperationException("The request to begin a time period was not completed because an unexpected error with code " + result + " occured.");
        }

        this.period = period;
    }

    internal static int MinimumPeriod
    {
        get
        {
            return timeCapabilities.wPeriodMin;
        }
    }

    internal static int MaximumPeriod
    {
        get
        {
            return timeCapabilities.wPeriodMax;
        }
    }

    internal int Period
    {
        get
        {
            if (this.disposed > 0)
            {
                throw new ObjectDisposedException("The time period instance has been disposed.");
            }

            return this.period;
        }
    }

    public void Dispose()
    {
        if (Interlocked.Increment(ref this.disposed) == 1)
        {
            timeEndPeriod(this.period);
            Interlocked.Decrement(ref inTimePeriod);
        }
        else
        {
            Interlocked.Decrement(ref this.disposed);
        }
    }

    [StructLayout(LayoutKind.Sequential)]
    private struct TIMECAPS
    {
        internal int wPeriodMin;

        internal int wPeriodMax;
    }
}

You can then use:

using (new TimePeriod(1))
{
    ////...
}

Nick