attractive weeds?

I'm not sure what these plants are, but looking more closely at the stuff that comes up on the edges of my lawn that I've been blithely mowing over.

This plant is very small, but something about its fine foliage reminds me of a rose. I stuck two of them in pots to see what they do.

This plant I've seen alongside trails in the nearby woods. I like its blue-green, silvery foliage

with a pale center. I also dug up two of these to observe closer- maybe it will turn into something aggressive or hideous, or someone can identify it for me.