1.? Rather too far away to see detail.

2. Stellaria media. Common Chickweed. Not Calyptocarpus vialis (sp)

3. Lamium purpureum. Red Dead Nettle

4. Artemisia vulgaris. Mugwort

Dig out 2 and 3 right now before they set seed. They're already in flower.

I think that 1 & 4 are the same, just cropped in #4.

Could well be.

1 & 2 are the same but 4 is definitely not the same. i'll try to get a better photo up. weed #1 might be chickweed. it has shallow roots & grows like a mat. I've been skimming a shovel & taking an inch of soil & it's coming up like sod. weed #4 has a deep tap root. it's getting treated with round up as it's in a smallish contained area. i'll look up mugwort.

took another look. I posted the photos out of order. I did a web search & it does look like photos 1 & 4 are mugwort, weed 2 is chickweed, & weed 3 is red dead nettle. reading up on mugwort it seems it repels moths so I have a perfect use for it. since it is aggressive ( in my yard anyway ) I have an area at the rear of my property where I have an erosion problem & the same area is near my bee hives. i'm going to try growing some there to check erosion & repel wax moths.

I numbered the plants according to the order in your post.

Mugwort will have no effect on moths outdoors in the garden. Any repellent effect it might have would only work in a closed environment like a closet against clothes moths. Much of the info on the web about supposed pest repellents is inaccurate, misinterpreted and regurgitated by bloggers and journalists whose do not access any original research.

Dig up the mugwort right away, also. It spreads by aggressive underground runners as well as by seed.