Need help with problem lawn

Our lawn has St. Augustine's grass. Photos of it are at http://www.geocities.com/tiggernut24/Birds/MyLawn/ - you will get a directory of photos.
First, is it pretty much suffering from shade stress, or should I look for more wrong? The grass is green and growing well where it is growing, but nowhere is it very thick, and there are large bare spots, and no grass at all grows near the tree trunks or the house.
Second, what kinds of St. Augustine's are most resistant to shade, that I should be readily able to find in Austin, Texas? Our grass also has to be able to tolerate drought.
I'm reading it both ways; is St. Augustine's easily killed by shade, or more resistant to shade than other varieties of grass?
Third, there are photos of some runners that are distinctly above the ground. I'm not sure if they originally grew that way or if they got more exposed than they originally were in the course of sweeping up bird seed over the winter. St. Augustine runners grow every which way including straight up. Should I cover these with dirt, or put a layer of dirt underneath them?
Fourth, should I till the bare patches to encourage grass to take root? The ground is hard but water is still able to soak in. I understand there are limited things you can do to loosen the earth on a lawn with St. Augustine's because you can damage the runners.
Fifth, how do I prepare teh bare patches for sods of grass?
Thanks!
Yours, Dora Smith Austin, Texas
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Dora Smith wrote:

It looks like shade issues with the growth. St Augustine is probably as good as it get for our shade turfs, but it still requires 5-6 hours of light. Thinning some of the limbs of the trees to allow more light filtering in can be a big help. Raise the height of the blade when mowing can also help.

Probably watering to help stimulate root growth will be fine.

Don't think tilling is necessary, the grass will migrate towards the wetter soil.

All have ever done is use a hoe to create a depression the size of the sod sheet, scraping it down to depth to where the sod is level with the rest of the yard, then watering.
Lar
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In the past, I've run across different subspecies of St. Augustine in web searches. Some do extremely well in shade. Some like more sun.
St. Augustine proliferates by runners. Many believe its seed can't germinate and grow. I'm neutral on that position as exceptions seem to be abound in nature.
Build up the soil with sandy loam and fine compost in bare areas. Keep it moist, do not overwater.
Do similar for laying sod. Just dig out just slightly larger than the piece of sod you're laying. Try to keep the surface of the sod the same level as adjacent established grass. Once established, water heavily once a week or so.
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