Schedule machine to wake up

You can use waitable timers to wake from a suspend or hibernate state. From what I can find, it is not possible to programmatically wake from normal shut down mode (soft off/S5), in that case, you need to specify a WakeOnRTC alarm in BIOS. To use waitable timers from C#, you need pInvoke. The import declarations are:

public delegate void TimerCompleteDelegate();

[DllImport("kernel32.dll", SetLastError = true)]
static extern IntPtr CreateWaitableTimer(IntPtr lpTimerAttributes, bool bManualReset, string lpTimerName);

[DllImport("kernel32.dll", SetLastError = true)]
static extern bool SetWaitableTimer(IntPtr hTimer, [In] ref long pDueTime, int lPeriod, TimerCompleteDelegate pfnCompletionRoutine, IntPtr pArgToCompletionRoutine, bool fResume);

[DllImport("kernel32.dll", SetLastError = true)]
public static extern bool CancelWaitableTimer(IntPtr hTimer);

You can use those functions in the following way:

public static IntPtr SetWakeAt(DateTime dt)
{
    TimerCompleteDelegate timerComplete = null;

    // read the manual for SetWaitableTimer to understand how this number is interpreted.
    long interval = dt.ToFileTimeUtc(); 
    IntPtr handle = CreateWaitableTimer(IntPtr.Zero, true, "WaitableTimer");
    SetWaitableTimer(handle, ref interval, 0, timerComplete, IntPtr.Zero, true);
    return handle;
}

You can then cancel the waitable timer with CancelWaitableTimer, using the returned handle as an argument.

Your program can hibernate and sleep using pInvoke:

[DllImport("powrprof.dll", SetLastError = true)]
[return: MarshalAs(UnmanagedType.Bool)]
private static extern bool SetSuspendState(bool hibernate, bool forceCritical, bool disableWakeEvent);

public static bool Hibernate()
{
    return SetSuspendState(true, false, false);
}

public static bool Sleep()
{
    return SetSuspendState(false, false, false);
}

Your system may not allow programs to let the computer enter hibernation. You can call the following method to allow hibernation:

public static bool EnableHibernate()
{
    Process p = new Process();
    p.StartInfo.FileName = "powercfg.exe";
    p.StartInfo.CreateNoWindow = true;
    p.StartInfo.WindowStyle = ProcessWindowStyle.Hidden;
    p.StartInfo.Arguments = "/hibernate on"; // this might be different in other locales
    return p.Start();
}