You really need to tell people where you live and what type of grass you have.

I didn't post what type of grass because I have no clue. It's new construction and its whatever the builder put down. It's in NJ

We can work with that. NJ is important because it is The Garden State. You have to be holding up your end of the bargain with the state chamber of commerce ;-)

Return the weed n feed. You can't use it in the summer without hurting the grass. Get a bag of alfalfa pellets (rabbit food) at your local feed store. You can fertilize with alfalfa pellets any day of the year. The application rate for alfalfa pellets is 20 pounds per 1,000 square feet. The fact that your dog's urine turns the grass green is a sign that the soil is basically healthy but needs to be fed. As you can see, the natural urine is a fertilizer. It works through a biological process instead of a chemical process. Alfalfa is also a fertilizer for similar reasons. It should turn your grass green in 3 weeks. Once you have the alfalfa down it should last the rest of the summer. If you missed some areas, you can go back and add more. This stuff is really fool proof unless you accidentally spill the bag. Then you can sweep it up and not hurt anything. As long as you do not bury the grass under a heaping pile of alfalfa, it will work for you. Also after you apply, moisten (not saturate) the pellets. Within 24 hours they will swell up and look like green worms. Follow up with a push broom or even just drag the hose across the yard and knock the worms down into the soil. Those worms are very fragile flakes of alfalfa. When the alfalfa is solid the birds can come in and steal them away. And no, alfalfa does not attract bunnies to your lawn. The only rabbits that eat rabbit pellets are those in captivity who have no other choice of fresh food.

Water your lawn deeply and infrequently. Deeply means one inch all at one time. Infrequently means 1x per week if the temps are in the 90s, once every 2 weeks if the temps are in the 80s, and once every 3 weeks if the temps are in the 70s.

Mowing height looks like it should be mid to high. There are very few grasses that do well when mowed at the lowest setting. Almost all of them improve when mowed at higher levels.

You can fertilize with organics any day of the year. You can fertilize with chemicals in the late spring, again in early fall, and again in late fall. You can also mix and match organic and chemicals without fear of overdosing. They work completely differently and do not interact.

Before your recommendation, I did some reading and went ahead with placing down some milorganite. Being in a country area out here in NJ, do I get alfalfa at horse supply stores ? Is there a big difference in me putting down milorganite or the alfalfa? What goes down in the late summer, early fall??