Question
Hi again
Westchester is a suburb of New York City.
Thanks for your great help.-------------------------
Followup To
Question -
I live in northern Westchester County and I have a lawn that has all three of the problems above. The lawn is about 1/4 acre altogether and the grass is in pretty poor shape, with small barren spots (this in addition to the issues I've already mentioned). I was planning on raking out my lawn now--it's early April--removing the moss by hand, then fertilizing, adding some lime pellets where the moss was and seeding. I think that any crabgrass removing stuff will have to wait until after the seeds I plant have germinated. I don't have a position on organic vs. chemical, though time constraints make me think that I'd prefer easy-to-use and fast acting chemicals.
Thanks
Answer -
Ji Bill;
You don't say what state Westchester County is in, so I have no idea what area you live in.
However, crabgrass is the same kind of problem anywhere.
It sets a good, deep root system, and flourishes.
All the crabgrass killers I ever tried also killed the grass in the area around where it was used, and the grass  didn't grow back as fast as the crabgrss did.
I always got on my hands and knees and dug it out by the roots with an asparagas cutter.
When I read the article about using dry molasses (sugar also works as well), and put down the sugar, the crabgrass began to disappear, along with the rest of the weeds.
Dry molasses and sugar DO NOT kill weeds. They keep the beneficial microbes alive so they work enriching the soil.
Fertilizers kill these microbes. Putting down the dry molasses, or sugar, counteracts the fertilizer effects and  keeps them alive.
Fertilizers nourish the vegetation growing in the soil, incliding the weeds. Then they wear out, and you have to fertilize again. Weeds love poor soil, they will not thrive in rich soil, so, make the soil rich, and the weeds will die out. In a few mowings there will be fewer weeds, and a few more mowings and you won't see weeds.
Put down the fertilizer, then put down sugar at the rate of 1 pound per 300 sq.ft, and water them both in together. In a few weeks there will be fewer weeds, but your grass will look lovely.
Since I started using sugar in the spring and again in the fall, I have not had to fertilize to keep a green, thick, lush lawn. and WEED FREE!!!
I had crabgrass, johnson grass, dollar weed. clover, dandelions, chickweed, and some others. Seeds blow in from everywhere, and seed. Pre-emergents will keep new seeds from germinating,but they will do nothing for the crabgrass etc that has already grown and set. they come back year after year.
Pre-emergents will keep everything from germanating. Bulbs, as well.
Meantime, if you don't want to wait fore the crabgrass to die out, you can dig it up by the roots. I used an asparagus cutter, slip it into the soil at an angle, and cut the root.
Sun is a good moss killer. It doesn't grow where there is sufficient sun. Removing some of the shade, but pruning out some tree limbs etc, will help the moss problem.
Try disolving baking soda in water and soaking the moss. I find this works better at killing fungii than all the chemical fungicides I ever used.
Organic is more about what you DON'T do, rather than what you do.
You don't have to be always putting something down to have a gorgeous lawn.
I put NOTHING down that will harm my beneficial soil living insects, and my lawn critters. Toads, grass snakes, and lizards. They keep the bad bugs eaten better than all the insecticides I used to put down, and I don't have to do a thing, just make sure nothing is put down to harm them.
Believe it or not. cockroaches are your friend. They naturally live in the soil, and they are better aerators than even earthworms. I can't stand the idea of one of them coming in my house, so I put fresh rosemary in my cupboard shelves, under sinks and cabimets, and appliances, anywhere they cam come in or hide, and I never see one in my house.
Termite remedies also kill the good guys. I put cedar bark in a trail around my foundation when it is time for them to swarm, and I never have to call the termite people, or get termite damage.
I spend so much less time and money, and have so much better lawn and garden.
I never see aphid damage on my roses anymore, or black spot mildew on them. Baking soda sprayed on the leaves, and underneath them, keep the blackspot away, and the lizards eat ALL the aphids.
If you would like more info about a good organic program, just write, and I will be glad to share.
Charlotte  

Answer
I didn't tell you about grubs.
North Texas is FULL of grubs and the Japanese beetles that are their adult stage. We call of them June bugs, because they come out of the ground and swarm in June, here.
My lizards eat them. Haven't had a grub problem since i got a good herd of lizards.
Charlotte