Best I can tell from the photo is chickweed and POA Annua. The chickweed is pretty easy. A little Ortho Clover, Chickweed and Oxalis killer should take care of that. The POA Annua is going to be a problem. A few treatments of Tenacity should do it but the seeds it is dropping right now are going to give you trouble for several years. A good pre m plan and careful use of Tenacity should keep it under control.

I'd say one of the dandelion look-alikes........perhaps Sonchus or Lactuca

You have to cook nettles. Their hairs are very irritating so must be cooked away. Even harvesting them or lightly brushing against them can cause a big problem, especially with some folks with super sensitive skin. Interesting side note, the inner pith of the nettle plant can be woven into fibers that are as fine as silk. In the old fairy tale about the princess with the six enchanted swan brothers, she is instructed by her fairy godmother to weave her brothers magic shirts from gathered nettle fibers to break the spell they are under and transform them back into princes. She must stay silent until the whole task is finished. The detail that is often left out of the "grim" story is that weaving nettle fibers could be a painful and time consuming task to do and stay silent the whole time. A real labor of love. Often other plants are substituted, but it's the wild nettle that makes sense in the story. And yet another side note, that's why you have to cook them, to get rid of the hairs and soften the fibers. To weave with them, you dry the plant and pound away the outer part of the plant, exposing the inner fibers.

Could be.... second photo is from too far a distance to be positive. Most broadleaved lawn weed killers will address this. Or you can always manually remove.