looking at the pictures the top one looks like a strawberry plant.
If you use herbicide it will kill almost everything and you're going to end up with a dirt patch until you reseed the grass. realistically that many weeds in the ground means it's deficient in pretty much all of the major minerals grass needs. Even if you kill the weeds and reseed with grass you're going to need to fertilize a lot to keep the grass strong enough to compete. Personally I'd leave it...
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