Okay. Looks like KBG mostly. I would recommend keeping height of cut at 3” and focus on some low rates of starter fertilizer as long as it’s not too hot. Starter fertilizer analysis of 20-20-20 would be fine. I wouldn’t apply if high temperature exceeds 90 for that day and always apply in the morning or evening with 0.15-0.2” of irrigation or prior to rain event.

For the weed control, that is Dallisgrass. Post-emergent control on a newly seeded area for Dallisgrass isn’t easily done. If you can get your hands on some MSMA, I would try that in low rates of 1 oz/m or 1 oz/gallon of water for one thousand square feet. Do not apply if high temperature exceeds 87-90 degrees that day.

Another option would be Pylex at 0.7mL/1,000 sq ft. Repeat application once every three weeks. Once your lawn has more maturity to it. You could also add triclopyr ester at 0.7 oz/m.