Strawberry-like weed in lawn

Would anyone know what kind of weed the photos below show? It's some kind of trefoil weed, I think, because the leaves come in sets of 3. And sometimes this weed produces a red thing that looks like a tiny strawberry.
You can see the thing resembling a strawberry in the first photo. Someone told me, though, that this weed is definitely not wild strawberry, but they don't know what the name of the weed is.
I'm also wondering if I should pull this weed out of my zoysia and fine fescue, or leave it? Is this weed nitrogen-fixing? I don't pull white clover out of the lawn because the clover is a beneficial nitrogen-fixer.
And the third question: What are those small yellow-orange spots on the bottom of one of the leaves in the third photo? Is it some kind of fungus? If so, can the fungus spread from the weed to the grass? If the fungus can spread to the grass, how would it spread--would it take simple contact or something else?
Here are the 3 photos:
http://imageshack.us/photo/my-images/510/strawberrylikeweed.jpg/
http://imageshack.us/photo/my-images/46/strawberrylikeweed2.jpg/
http://imageshack.us/photo/my-images/577/strawberrylikeweed3.jpg/
Thanks very much.
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ZoysiaSod said:

Don't ask advice from that person anymore. ;)

It's not a legume.

The photo's out of focus, but they look like aphids to me.
--

Eggs

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I found the answer to my first question. This weed is called "Indian mock-strawberry" (Duchesnea indica), according to the Weed I.D. guide found at: http://weedid.missouri.edu//weedinfo.cfm?weed_id
The link above to the University of Missouri's weed I.D. guide provides some excellent photos of this weed. The University's guide is awesome--very well done.
This weed differs from wild strawberry in several ways, among them is the color of the flower. Wild strawberry has a white flower whereas Indian mock-strawberry has a yellow flower. (Great photo of the flower on the site too.)
This is a perennial weed with stolons.
Eggs Zachtly, thanks for answering Question numbers 2 and 3 though.
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On 11/19/2011 4:08 PM, ZoysiaSod wrote:

Very hard to tell anything from those out of focus pictures.
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