Since the leaves are kind of round, I'd say they're weeds. The problem is that there's no way to pull them without walking on the lawn, which can be detrimental to the grass.

I'd pull weeds you can reach (being careful to avoid any grass that may be sprouting) but leave the rest and deal with them once the lawn is established enough to do so.

Oh they're DEFINITELY weeds. I don't have the name of the tip of my tongue, but I get that stuff all the time in my garden and by my A/C unit. I roundup it routinely. I agree with the above. Let the grass come in and hopefully that will crowd out those pesky weeds. If not, then you can use a lawn-safe weed control.

I shouldn't walk on my lawn?!!!

That's the only way I can get sprinklers out there. I don't have an in ground sprinkler system.

Well, you walk on that newly sprouted grass and you'll flatten and probably decimate most of it. If it's an area that is simply overseeded, then that's fine. The other grass is enough protection. But on bare spots? No...you need to stay off of it. I even rope off sections of my lawn if they are not "grassy" enough by Halloween. Don't want the kids tromping it.

Definitely need to stay off of it as much as possible while doing a re-seed.

I laid out flat sprinkler type hoses that I didn't have to move once to keep a re-seed moist when I didn't have sprinkler system.

If you don't try that, you might buy an extra sprinkler or two and hose to cut down on foot traffic while watering? Move the hose from the sidewalk, beds, etc?

OK, so seedlings are coming up everywhere. Moreso in the shady areas which were seeded with a "Rebel shade grass" mixture of fescue.

I haven't done anything about the no walking on grass issue besides trying to walk as softly and with as little shear force as possible. I am still moving sprinklers, but I try to walk as little as possible on the grass. I will let you know how it goes and should be posting pics to keep you updated.