The bermuda will win against the fescue, and the sledgehammer label should tell you how long after establishment to wait before applying. (You can google for the label before buying, even.)

Clays are interesting soils. They hold by far the largest amount of water, but release only modest amounts to the plants (the rest binds rather tightly to the particles). Silt's actually got the best plant available water characteristics. During spring, it tends to be soaking wet, low oxygen, and sticky. During summer, dry, higher oxygen, and given to runoff. Fall varies, but tends to be more like summer than spring. It has the least air penetration, so root systems tend to be no great shakes. Combine that with the lesser water availability and you have a problem. That can be ameliorated with plenty of OM and plenty of soil life. Earthworms will happily dig down several feet to make their homes (the primary species here can go six feet down easily). Clay tightens up and deflocculates if you look at it funny. Fortunately, there's enough calcium here that it's unlikely to happen, but I'd still use shampoo once a year if it were me. That'll help with water and air penetration as well. All things considered? I'd rather deal with pure sand than heavy clay, but you get what you get.

Seed heads are why people sometimes have to mow their bermuda 2x-3x per week. Your lawn is very normal. Your version of the correct mowing height is at the far upper end of being practical. That height is used because most rotary mowers can't go any lower, but if you had a reel type mower, 1/2 to 3/4 inch would be better. When bermuda is kept very low it takes on a different growth habit and becomes more dense. If you ever visit a golf course, look at the greens and how the grass stems grow sideways with the blades coming off the stem. Most residential bermuda lawns have vertical stems.

Gavin, that's crabgrass. The reason you have it is your care program. The biggest encouragement to crabgrass is the daily watering, but it still would have trouble getting started if you weren't mowing so high and infrequently. Tall bermuda is thin and allows plenty of sunlight down to the soil where the weed sprouts need it. The clover looking weed is oxalis. You can kill that with Weed-B-Gone Chickweed, Clover, and Oxalis killer. Be sure it's safe for bermuda lawns first. You would be much better off with the following care routine: Weekly Mow every other day at 1/2 to 1 inch high. Bermuda should be mowed low to become the most dense. Picture the density of a putting green mowed at 3/16-inch high. Mowing at 1/2 inch is almost that good. Water once but apply a full inch. Time how long it takes to apply a full inch by setting out cat food or tuna cans around the yard. Time how long it takes to fill the cans and that's your new watering time. If you're still in the heat wave of last weekend, you could water once every 5 days, but when it gets back down below 105 and into the 90s, then once every 7 days should be enough. This works. I was in Tempe and Gilbert last weekend and visited a friend with St Augustine. He waters once every week and it's still too much. He's got disease issues from too much water. If he can do it with St Aug, you can do it with bermuda. When the temps drop into the 80s, back off to once every 2 weeks. When you allow the surface of the soil to dry out completely before watering again, the crabgrass seed cannot germinate. Monthly High nitrogen, low everything else, fertilizer. If you decide that this level of care is more effort than you want to put in, then you might consider switching to St Augustine. That's what my buddy in Gilbert did and he's happy. With St Aug you only fertilize 3x per year and only mow once a week or two. St Aug is a coarse bladed grass like crabgrass and likes to be mowed very high (opposite of bermuda). Paul, that looks like hybrid bermuda on the left and common bermuda on the right. Are you sure it's not just the two grasses mingling that looks weedy?