The second plant may be Alternanthera philoxeroides. The third one is one of the Stork's-bill species, such as Erodium cicutarium.

I think 2 is Sarcococca confusa, sweet box

#4 Cornus mas, Corneliancherry dogwood

First pic also has a chickweed flower on the right side.

Thank you, guys! The Stork's Bill= Redstem Filaree (http://www.colostate.edu/Dept/CoopExt/4DMG/Weed/redstem.htm)?
Sarcococca confusa is spot-on, as is
Cornus mas. As for the viola specie.. I don't think it's the common blue violet, (leaves oblong rather than heart shaped), but will try to get a better picture just to make sure.

Two white violets with lanceolate leaves in your area are Viola primulifolia and Viola lanceolata.

Is everyone convinced it is a Violet? I can't see any violet buds or leaves - of any shape - in the photo. The one bud I can see clearly doesn't look right. I'm reserving judgement until I see more pictures.

UPDATE: Here's more of those mystery violas! (Plus a bonus mystery flower)

Edit: Nevermind, looked up and it looks to be

Viola bicolor. Still wondering what the yellow thing is, though.

Yellow one looks like a Cordydalis. I'd say C cheilanthifolia if pushed to specify.

I looked up Maymont and found it was a museum and public park. Was it OK to pull up plants? Or were they selling them?

Thanks for the ID! Thinking it's a yellow fumewart.

The latter violets were pulled off of a grassy strip between a public sidewalk and a public road, not from Maymont grounds. I figure, since they were not protected/technically weeds, the city of Richmond wouldn't miss a couple. ;)