My guess is some type of Oenothera triloba.

If you would collect seed later., I would not mind some. I would love some if you would like to trade. By summers end I should have other Oenotheras. I , too, love to garden with weeds.

Looks like Oenothera to me, also. Check that bud in the evening--it will open to a beautiful yellow "primrose". Fine plant for native gardens. If you save it, dig deep--it's got a taproot.

I don't have a facebook account but can see your photos on the site. If you can post them here so people can comment without having to go back and forth it will help.

The Oenothera triloba has been ID'd. It's native and supports all the nocturnal moths, I'd leave it alone.

The big thistle like thing you don't like is probably a non native thistle of the Sonchus genus.

The low thing with the purple flowers is Sherardia arvensis, common name Sherardia, non native.

The low thing you said you like because you don't have to mow it appears to be a plantain, some are native some are introduced.

The one you call a dandelion does seem to be a member of the genus Taraxucum.

Your "fern" is something in carrot family probably Torilis arvensis.

Hope this helps.