I'll follow up the photo of the horse with my suggestions for organic lawn fertilizer, but my suggestions refer to what goes into a horse, not what comes out.
Twice a year I feed my lawn like a horse: I give it soybean meal in the spring, alfalfa pellets in the fall, both of which I pick up at a local feed store, usually for less than $20 for a 50 lb. bag. Apply at 10-20 pounds per 1000 square feet. This feeds the microbes in the soil, which in turn, feed the lawn. I also use a mulching mower and mow at the highest setting that will provide a manicured look. The result is that I have the best looking lawn in the neighborhood.
Weeds, I usually manually pull them as I spot them. Dandelions are the main culprit in my lawn, which are relatively easy to maintain if you don't let them get a foothold. Oxalis is more difficult, but Bayer makes a product for broad-leafed weeds called Natria Lawn Weed Killer. It's derived from iron and is reportedly more environmentally friendly than most weed killers. That might be worth checking out. Vinegar is also a good organic weed killer, but it's not selective and will kill just about anything you spray it on, including your lawn.
Best o' luck with your lawn.