some are weeds, probably crab grass, and some are lettuce. for example, mapping the picture onto (0,1) in x and (0,1) in y, the group at (0.7,0.3) is mostly lettuce. the group at (0.2,0.8) is mostly crabgrass. you have crab grass in the spinach picture too, with very little spinach (not uncommon, spinach are slow germinators, specially in warm soil).

I learned long ago that you really need to plant this stuff in rows about 2" wide and than have 6" to 8" between the rows so you can get 3 to 4 rows in a 4' wide bed. The rows need to be far enough apart to easily get a hoe in there so that weeding does not consume hours of your day trying to keep the salad bed clean (and they do need to be clean, especially if selling to chefs). Plus I have found that most of the greens do better with some space on either side. When I have done dense planting I always seem to have portions damp off, leaving holes in the bed and a place for weeds to take hold.

Something in the Brassicaceae, maybe a gone to seed radish or turnip - or one of the many wild members of the cabbage family.

One of my favorite books, now passed on to a horticultural library, concerned farming in MA during the Civil War. Several pages are devoted to eradicating this thistle which always has been a costly, troublesome weed. The 'solution' then was to mow grasslands in the fall to a height of about 6" which left the hollow centers of each thistle exposed to the winter elements which killed the plant. Based on this writing and years of experimenting when living in Yankee land, I dealt with the thistle by cutting each stalk back to about 3" in height during active late spring growth and placing 2 drops of clorox into the exposed hollow stem. Clorox keeps on working and will slowly kill the extensive root system. Patience! Hand pull the weed near your prized tree as even a single drop of clorox is effective for quite a radius around a treated plant. And, if the decision is made to use no chemicals then remove each thistle, cutting below soil surface. Repeat until root system dies off. Try using a linoleum knife as a "down on the knees" weeding tool. Most effective weed controller I have in my gardening tool kit.