Practical Alternative for Windows Scheduled Tasks (small shop)
Consider Cygwin and its version of "cron". It meets requirements #1 thru 4 (though without a nice UI for #3.)
Apologize for kicking up the dust here on a very old thread. But I couldn't disagree more with what's been presented here.
Scheduled tasks in Windows are AWESOME (a %^#% load better than writing services I might add). Yes, not without limitations. But still extremely powerful. I rely on them in earnest for a variety of different things.
If you even have a slight grasp on c# you can write as custom "task" (essentially a console application) to do, well, virtually anything. If persistent/accessible logging is what you're after, why not something like Serilog or NLog? Even at the time of writing, it had a very robust feature set. This tool in and of itself, in conjunction with some c#, could've solved both your problems very easily.
Perhaps I'm missing the point, but it seems to me that this isn't really a problem. At least not anymore...