Look up shepherd's purse, Capsella bursa-pastoris. The seeds look quite a lot like your first picture, though maybe not exactly, so maybe it's a close relative. It is a very common weed in different continents.

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.

Yep

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.