Yeah, you have bermuda in there, and that is what you want. Honestly, you could blanket spray that whole yard with a 2% roundup solution, kill most of those weed's (roundup doesn't kill everything) (spot spray anything else with 2-4,D) and the bermuda will survive, it will set it back 4-6 week's but it will survive. Bermudagrass is so tough that gassing it with methyl bromide(a super strong sterilant) doesn't alway's kill it. And reseed with Princess77 (the best bermuda seed) one week later. Seed at three Lbs. per 1000 sq. ft. Keep that seed wet for 4-6 week's so the seed can germinate (bermuda germinate's slowly, don't let that worry you) and get going, and you will have a yard that is at it's greenest in August, is thick enough to choke out most weed's and require's minimal irrigation. You do need to get a soil test, i'll bet your nutrient levels are low, you are on that red clay right? These people are excellent resource's for that and any other outdoor issue you might have.
This is some general bermuda info for you, just don't use any pre-emergent herbicide's the first year.
If you have any question's, just ask. Good luck.