[GpsFrontier]

Ya, when the pump shouts off the water will syphon back into the resevar through the pump.

should they be flush with the bottom of the bucket or is it okay to leave a bit of length inside so there is maybe 1/4 inch or so water in the bucket when fully drained?

There is no need for it to be flush with the bottom. Actually that's why I was suggesting using the through holes so that the water level inside (both flooded and when drained) would be adjustable. That way you would be able to change the water level when needed as the plants are growing. The way I would do it is have the water level when drained about 2 inches below the bottom of the bucket with the plants in it. Then as the plants roots grew down into the water start lowering the water level (when drained), so that abut half of the hanging roots are always in the water. Then finally I would set the water level (when drained) so there was always 3 to 4 inches of water at the bottom. That's just the way I would do it, but you can do it however you wanted.

As for the air stones within the buckets, is it alright to have them in the buckets only with no aeration in the nutrient solution tub?

The only benefit to having it in the reservoir rather than the buckets would be to inhibit algae growth in the reservoir. But if the reservoir is light proof algae wouldn't be able to grow anyway. Also keep in mind that my suggestion of having the air stones in the buckets is based on there being at least a few inches of water in the buckets when drained (at all times). If there is not going to be water at the bottom of the buckets, I would then have the air stones in the reservoir.

Also, is it safe to keep some lava rock in the bottom of the buckets so that it doesn't take so much water to fill the buckets, allowing for a quicker flood and longer nutrient soaks?

It would be safe as long as there is no possibility of them clogging your flood and overflow tubing. Although if the reasoning is to allow it to fill quicker so they can soak longer, that can be done by the timer settings also (longer on time). But the down side to having such rock at the bottom is that as the roots grow down and reach the lava rock they will cling to it. So lifting the lid to get inside the buckets will likely rip or damage some of the roots, and/or move the rock in a position that may clog the tubing. If the idea is to take up space so the system uses less water, I would probably just use a couple of bricks. There is less surface area for the roots to cling to, and it's a solid object (not porous) displacing more water than the lava rock would.

The timer I bought will time down to the seconds, which is awesome...I just have to figure out if it will allow me to put constant power to my air pump, and switched/timed power to my water pump.

Sounds like it is a digital timer. I don't know your timer but just a note that I found out about my digital timer. The package said up to 144 settings but tell this day I have not figured out how to get more than 14 on/off cycles out of it. Even 14 X 7 days is only = 98, so I don't know if it's just me or not. I just have an adapter that splits one plug into three plugs, the timer plugs into one plug and the air pump plugs into the other. That way the air pump has power 24/7.