Uncertain about #1. But #2 looks suspiciously like garlic mustard, a nasty invasive weed that's rapidly taking over the understory in many regions. If so, get rid of it now.

See http://www.invasive.org/eastern/biocontrol/29GarlicMustard.html

Here is a link that might be useful: garlic mustard

#1 looks like a member of the genus Heracleum, cow parsnips. There are several that have a similar appearance.
hortster

I now know that the first weed is in fact Cow Parsnips. However, I'm still confused as to what the second weed is. It grows a lot in the shade.

I think the second plant is catnip.

Mary