Those brown/tan spots are grey leaf spot (fungus). What time of day are you watering? Always water early in the morning, if possible. Evening watering encourages fungal problems.

More important than the fuzz are the brown lesions on the grass blades in pictures 2 and 3. Mushrooms mean you have far too much water. At this point it is too late to adjust the water and get rid of the disease. If you have the Floratam variety of St Aug, it will fight back but will take a long time to fully recover.

I have had success with this type of fungus by using ordinary corn meal applied at a rate of 20 pounds per 1,000 square feet. You can buy corn meal at feed stores in 50 pound sacks for under $10. Call first to be sure they have it. Corn meal works biologically rather than chemically. Corn is decomposed by various fungi. One of the fungi that comes in with the decomposition is a predatory fungus. It feeds on other fungi including the one that causes the disease you are seeing. Apply the corn meal now and in 3 weeks you should see the browning stop and no more lesions.

If you cannot find corn meal at a feed store then buy corn flour at a grocery store catering to Hispanic shoppers. Cost should be $7 for a 25-pound bag. Be sure you don't get the stuff with baking powder in it. That's like the Bisquick for making tortillas. You want the plain corn flour, masa de maiz. Maseca is a popular brand.

You should back way off on watering frequency. I would give it a week to dry out watching for wilting. In fact I might go until it starts to wilt somewhere just to make sure it is dry enough to water. Then start with deep watering. Start with 1/2 inch of water, twice a week. If it rains, don't water for a week or possibly longer depending on how many inches of rain you got. When this is mature it should easily go a week in the summer heat without watering.