If your going to use a herbiced I would spot spray only. (read the label carefully) Proper management practices that encourage a dense, thriving turf are the best method of weed control. Healthy turf shades the soil so sunlight can't reach weed seeds ready to germinate. A thick turf also minimizes the physical space available for weeds to become established. There are several management practices that will promote a healthy, dense grass. If turf is over-or under-watered, over-or under-fertilized, or mowed too low or too infrequently, the turf is weakened and cannot compete with weeds. Damaged areas resulting from using unsharpened mowers increase time needed for turf recovery, allowing for weed invasion. It is very important to understand that weeds don't create a void, they fill a void. Mulch Mow High 4+" with a sharp, balanced blade Water deeply and infrequently with 3/4-1" water. (no more than once a week in summer) What variety of grass do you have? When was the last time you fertilized?

Chickweed. It can only get a root hold on bare soil so if you can improve the lawn the chickweed should go. Meanwhile try to pull as much as possible before it drops all those seeds.

There's a grass called Kyllinga which I've never seen personally. Compare with images of that.

What are you considering "the weed" in the picture. Is it the broadleaf plant or the yellow tipped grassy plant? The yellow tipped grass looks like the seed head on buffalo grass to me. If you are watering daily, stop that. Watering too frequently will turn a lawn yellow. Here's a picture from morpheuspa of his Kentucky bluegrass lawn versus the other KBG lawns in his neighborhood. He watered his once a week while the others watered every day. If you are currently watering every day, you'll have to wean it off of frequent watering to get up to deep and infrequent watering. I'll give you the deets on that if you want or you could look for 'deep and infrequent' in this forum.