I don't think it's crabgrass. It's not warm enough yet for crabgrass. I think it might be tall fescue mixed in with a predominately Kentucky bluegrass (KBG) lawn.

I think if I were you, I'd concentrate on improving the soil and trying to get the lawn as healthy as possible between now and the end of summer. Mow at about 3.5-4 inches and always mulch mow. Water only when the grass really needs it (try to go for a week at a time, and longer if you get rain) and when you do water, water deeply. If you can add any organic matter (compost, shredded trees that might be available for free from tree trimming companies, used coffee grounds from Starbucks, etc).

You can get rid of the broadleaf weeds using a broadleaf weed killer (usually something with 2,4 D) and/or a weed hound (available at most big box stores). I avoid the weed and feed products for a couple of reasons. It's better to fertilize and kill weeds separately. Fertilize first to get the weeds growing well, then spot spray them with the weed killer while they're healthy and more likely to take in the weed killer. You'll need to hit the fescue with glyphosate or dig it up. Anything that will kill it will also kill the KBG, so you'll have dead spots until you reseed in the fall.

In late summer, when the heat breaks, mow the existing grass as low as you can and overseed with good quality KBG seed. If you want a really elite lawn, kill the existing lawn first with glyphosate (brand name roundup) before seeding. Then keep it damp for about three weeks, watering as often as three times a day for a few minutes at a time. After the new grass germinates, start cutting back on the frequency and increasing the length of time you water until you're back to once a week watering.

Here are your pictures

I'd do what bpgreen says. Just maintain and have patience over the summer. Mow at your mower's highest setting for the summer. If you seed now, you are guaranteed to have a full crabgrass lawn by August.

I fertilize with ordinary corn meal and alfalfa pellets (rabbit food) from my local feed store. In your area you might be able to find soybean meal cheaper than corn. Apply at the rate of 10-20 pounds per 1,000 square feet. If you want to do that you can apply now, again on 4th of July, and again on Labor Day. By Labor Day you should be ready to go with your reseeding plans.

Go to Google and do the following search

"Kentucky bluegrass" blend Bedazzled Brilliant Kingfisher bewitched

Look at any pictures you see of the Elite Kentucky bluegrasses. They are awe inspiring.

One more thing from your second picture. Do you see the gigantic circle in the middle of the picture? It's about 15 feet across. That was caused by a fungal disease some time in the past. It started small and killed all the grass in the circle as it spread out. Watch for those now that you know your lawn is susceptible. AS SOON AS you see a perfect circle happening, whether the grass seems to be affected or not, you need to think FUNGUS. One of the reasons I started using ordinary corn meal is that it is the organic solution to fungal diseases. It is not a fungicide but it attracts other fungi that are fungal predators. Basically you apply ordinary corn meal and three weeks later your grass is growing back. The scientific research on this is only preliminary, but the experience of those here on the forums is overwhelmingly positive.

The pictures might be deceiving but is the center of that circle in the second picture a low spot? If so, and since your mailbox looks to be low by the street, I would suggest you consider having your entire property regraded in preparation for the new lawn in August/Sept. Regrading goes very fast when they use a tractor and box blade. It will leave you with the perfect surface and perfect drainage for new seed.