dchall, reeljake and couple of others can advise you regarding your warm season turf, but you'll need to tell them what grass you have. Common types are bermuda, centipede and zoysia. EDIT: and St. Augustine. If you don't know use this.

Pictures help. Post some close enough to see the individual blades.

And take pictures on a cloudy day if you can. 3 inches is a good distance.

Wait until April to spot spray the weeds with Weed-b-Gon or Weed-b-Gon Chickweed, Clover, and Oxalis Killer or equivalent. That gives the grass and weeds time to get a little healthier.

Don't fertilize until Memorial Day.

Don't use weed n feed (EVER). Why? Because note that weed killing is done in April while fertilizer goes down a month and a half later. You don't do both at the same time like wnf products do.

Don't buy and lawn seed until you know what you have. The only (popular) southern lawn type that takes seed is common bermuda. Hybrid bermudas should not have common bermuda seed mixed in.

No matter what warm season grass you have, it spreads. If it looks dormant or thin now, it will perk up very soon and fill all by itself.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

I aerated one of my lawns in the past 50 years. It did not improve anything when I did that. What finally fixed the lawn was fixing the watering and switching to organic fertilizer.

Mowing height recommendation will come after we know what kind of grass you have.