You can level bermuda either in the hottest heat of summer or in the coldest dormancy of winter. Fall is not great because you will be smothering a living lawn. Having said that, if you try to fill more than 2 inches at once, you might smother even a dormant lawn. So if you can identify the spots that need a lot of sand and start to fill those now, that would really help things along. You can full all the way up until the soil is level as long as you leave living grass showing up above the fill sand. What kills the bermuda is blanketing out the sunlight. So you could fill up a low spot and then start to brush away the surface of the fill until you have grass showing. One-half inch would be plenty showing, but anything that's buried might not come back.

We like pure sand because topsoil always has clods in it. When you start dragging clods across a perfectly level surface then you have furrows instead of smooth. Even 1/4-inch clods make mess. If you could pulverize all the clods then topsoil would be fine.

Your coverage immediately at the base of the tree is fine. You should have the tops of the roots exposed at least an inch away from the trunk of the tree. But those long roots out away should be covered.

The pic showing the sprinkler head next to the house is interesting. The distance from the bottom of the brick to the soil should be at least 4 inches. It looks like you might have about 6 inches. That is fine, but if you bring it up, use 4 inches as your minimum gap there.

Have you read the topics on leveling with something like a chain link drag? Basically you scalp the lawn down, spread sand, drag the drag until you get it like you want, water to settle the sand, recheck and add more sand as you find low spots, water to settle, recheck, etc. Then don't touch anything until the grass comes in. Doing the job in the summer means the grass will grow right back. Doing it in the winter means you have to keep off the sand until April or so.

Also if you add more soil, the grade should fall away from the house a minimum of 6 inches at 10 feet away from the house.

Thanks Dchall. I figured if anyone would respond to this then it'd be you. I've read lots of topics on the procedure for this and will definitely follow those. I just didn't remember coming across any where someone needed to add as much sand as me and I didn't know if any other steps were required. It looks like the same procedure though with just slowly adding over time.