If you're in the US, contact your county's Extension Service office because they will know the common weedy plants in your region. Locate that office with this interactive map: http://npic.orst.edu/pest/countyext.htm

Sharon, your first pic is not Purslane,(Portulaca), it's chickweed,(Stellaria). It would probably be good for rabbits, because it's edible and nutritious for humans. The second plant is not Echinacea, It's goldenrod, (Solidago). They are native plants, but some, like the one you have, are weedy and invasive. The seeds blow in on the wind, and they can take over a garden in no time because of their fast spreading root system. When removing them you have to comepletely remove all the roots, or it will just come back. I don't know if goldenrod is good for rabbits or not, but the wild rabbits in my yard never eat it. I can remove all the goldenrod each year, but the next spring there is always more. Your third plant looks like a weedy Veronica. Most species of Veronica are edible and healthful so you can try those for the rabbits. Some Veronicas taste like watercress. I live in Joliet, 40 miles south of Chicago.Sharon, it's kind of puzzleing what the wild rabbits in my yard are eating. They sometimes munch on the legumes, but I haven't seen any damage this year. I went to pull up a horseradish stalk I was trying to get rid of, and there was a bunny nest under it's large basal leaves, so I left it undisturbed. I heard you can grow new carrots from the tops that still have leaves, so I tried it, and the next morning I discovered the rabbits had eaten every last one of them. I guess they really love carrot leaves, though I'm also guessing that eating too many carrot roots is not good for them. Purslane is a weed that might make it to your yard on its own. Echinacea you would have to aquire. If you did have Echinacea last year, it may yet be still alive and choking inside the huge clump of Solidagos. Echinaceas don't do well if they are crowded by nearby taller plants.

Try comparing to Veronica persica for #3. I see you have some dandelion in #2, I would expect them to be bunny edible. If you have dandelion, chickweed, veronica, etc., it is obvious that you have broadleaf weeds and so I would look for plantain (Plantago spp.). Probably another one you can feed the bunnies.

Sort of looks like bind weed. Looks enough like it that I would try killing it the same way I did with the bind weed. Assuming you want to get rid of it, try this: find a bud vase, fill it half way with straight RoundUp (I used 42% strength), dip one tendril of the weed into the RU and leave it there. You might have to block up the bud vase to keep it from falling over. I don't know how long to let it sit like this, but when I did it for a few weeks, it killed the entire plant. You may have more than one plant, but bind weed grows from one central tap root. I killed 300 square feet of plant with one dip. This approach is very minimal impact even if you hate RoundUp. Only one plant gets treated.