Very small and young, so can't be sure. Maybe - jewelweed (Impatiens spp.) If so, can get over 3' tall. Possible ID based on one leaf in center of picture, lowest. Looks like jewelweed.
hortster

Here is a link that might be useful:

First is Jewelweed. Really good for butterflys and hummers. Also great to spread on your skin if you get poison ivy. Always try on your skin before using to see if you have a problem with the gel.

Second is a type of dock. Use a long knife and cut the roots way underground. If the root turns yellow it is similar to the burdock that you can purchase in many grocery stores.

3 I am not certain but appears similar to Virginia Bluebells. However you have a much worse problem at the base of the picture, vinca. Vinca will take over everything including climbing trees and will with time be the only plant there. We have it across the street and other than providing cover for a few creatures there is no use for it.

4-5 Your plant may be lesser celadine because you mention flowers.

Rather than getting rid of the things you have pictured most would be trying to divide to have more to plant.

Oh, its not vinca, at least not what I was told anyway. I was told it is a type of climbing Euonimous and its doing its job. It is climbing the dogwood tree, but the dogwood only has a few good years left in her anyway, she's very old and on her way out. The euonymous or vinca, whatever it is, is there to climb in and around and throughout our dry stack stone wall and its working quite well!

The last two are celendine poppies and I found out that the second one in question is a slightly different variety.

I'll have to check out this jewelweed and the virginia bluebells!

Just so you know I have attached an article about the spreading quality of your plant. It may be doing it's job where it is at but you will shortly be seeing baby plants every where.

Here is a link that might be useful: Mobot