Thank you for doing your homework on the questions we were sure to ask.

Lawn care is relatively simple. Water, mow, and fertilize. You do not automatically need lime, insecticide (grub control), herbicide (weed control), or fungicide (disease control).

Let's start with watering. You are watering too often. By not allowing the soil surface to completely dry out you are inviting weed seeds to germinate. You are also not allowing your grass roots to grow deep into the soil. This causes your grass to become dependent on frequent watering because the shallow roots cannot get to the any water deeper in the ground. Furthermore, and the worst possibility, the wet soil will cut off air to the microbes in the soil allowing disease to take over. To improve your watering, first measure how long it takes to apply a full inch of water. Do this using cat food or tuna cans placed around the yard. Turn on the sprinkler and time how long it takes to fill most of the cans. Use that as your starting point. At this time of year in Ohio you should only be watering once every 2-3 weeks. I live in the Texas desert and am still only watering once a month. When you do water, apply a full inch all at one time. At first you cannot go cold turkey into this. Watch your grass for signs of dryness. Try to go as long as you can before you see it dry out. If it goes a full week, water deeply immediately. Then see how long it goes before it needs it again. If it needs it sooner than 2 weeks, water more deeply. But start with one inch. Eventually you will train your roots to grow deeper and pick up the deeper water down in the soil. Deep moisture stays there longer because the soil temp is cooler and evaporation is reduced.

Mowing is the next concern. I like to keep mowing heights very simple. Some people split hairs and will tell you to mow at 2 5/8 inch but not 2 1/2 or 2 3/4. I'm not at all that picky. I have two setting suggestions: the lowest setting on your mower (bermuda, bent, and centipede) and the highest setting on your mower (all the rest of the grasses). That's about as simple as it gets. Mulch mow weekly unless the grass is growing too fast. Then mulch mow 2x per week to keep up with it. These settings for these grasses will give you the most grass density, shade the soil, and help prevent weeds. If you get the wrong setting for the grass, you open up the problems. Also dense grass needs less water. And tall grass does not grow faster than short grass. My mower is set to 4 inches. When the grass gets to 5 inches, I mow. Takes about a week to grow an inch.

Fertilizer. If you are using chemical fertilizer, put it down once in late spring (NOW! Memorial Day) and twice in the fall. Labor Day and Thanksgiving are good. Follow the recommendation on the bag. If you want to use organic fertilizer, you can apply that any day of the year in practically any amount starting at 15 pounds per 1,000 square feet. A better app rate is 20 pounds per 1,000 and you can go up to 80 pounds if your wallet allows. When you get above 80 pounds per 1,000 you start to smother the grass with fertilizer. Also you get a strong aroma (stench) of decaying protein if you use too much at once. Start small and you may notice the smell but it will not be bad.

If you follow those guidelines you should not have to worry about weeds, disease, or insects.

Grass types:
Fescue is a northern type grass. You likely have some in your lawn. Fescue is a bunch type grass that grows only in small bunches. It does not spread fast. Thus if you want a dense fescue turf you have to apply lots of seed. Fescue is the only northern grass that will tolerate shade.

Kentucky bluegrass is another one you might have. It is a sod-forming type grass which spreads (and spreads and spreads). In theory you only need one plant and you can have an entire lawn form as it spreads out. If you have a mix of fescue and KBG, the KBG will eventually dominate simply because the fescue cannot spread to fill in areas which might die out for some reason. KBG is not tolerant of shade at all. If you have trees in the yard KBG would thin out and possibly not grow at all depending on the amount of shade.

Insecticide. The problem most people report is grubs. Grubs are in everyone's soil. As long as you have fewer than a dozen grubs per square foot, your grass should tolerate them. If you have more, then it might be time to do something. But before you have grubs you have to have an infestation of Japanese beetles or June bugs. You will notice them swarming your porch lights in May and June. If you do not notice that phenomenon, then you likely will not have enough grubs to cause a problem. If you do see them swarming, wait a month for them to bury their eggs and then apply something like Grubex or beneficial nematodes. Late July is the normal time to apply something for grubs.

Wow. Thanks for the info!!!
I've just put a small container on my yard to measure the amount of water.

By the way, are these really fescue? I read through the forum and "Poa Annua" and "creeping bentgrass" caught my attention. This area was lighter green before the first mowing and after the mowing started, the area has become brownish. The seed portion has purple color. There's another kind of grass which is more like all over the place (unlike this purple ones that are in that rectangular area) that has similar seeds (flowers?) but the color is white.

I receive chemical fertilizer four times: first with crabgrass preemergent, second in June (slow release whatever that means), third in the fall, and fourth in the late fall. So it seems the program is in accordance with your recommendation.

Also, I'd take it as I don't need the "insecticide" other than the grub control I'm already receiving?

Going to Lowe's to return the "SNAP" system. haha

Here is a link that might be useful: insecticide I was talking about