1 cubic yard will cover 1000/ft2 1/4 inch

This is just my thoughts running rampant, I'm no expert, but since your main issue at the moment seems to be the soil's lack of ability to absorb water, I'm thinking water as deeply as you can just prior to aeration to soften the ground to make it easier for the plugs on the aerator to penetrate the hard soil. Then after aeration, water again to let the holes fill with water and soak into the soil before you top dress with sand. The sand should fill in the holes left by the aerator and eventually work into the soil and help change its structure to something that'll absorb water better. From everything I've read about top dressing, its best to add no more than 1/4 to 1/3 of an inch at a time, more than that could smother the roots.

One more question. Is it ok for me to level my yard with sand now, or should I wait until next spring to do it? If there isn't a very compelling reason to wait, I would rather do it now.

http://www.levellawns.com/top_dressing_video.aspx

Here's a video of a service doing it.
1. scalp
2. aerate
3. fert
4. sand
5. drag

I've honestly never seen or heard of anyone doing it to dormant grass. I'm doing mine around the 4 th.