Someone else had better do #1 for sure. It has an appearance that could be oxeye daisy, which is both a garden flower and noxious weed, but I really don't know.

The second looks to be a cucurbit and I think I see a spiny fruit in there somewhere, so it could be wild cucumber. Doesn't grow in my area, so I've never seen it, however by the look of the leaves and vines, I would think Round-up or 2,4-D would control it, though repeated applications would probably be necessary to eliminate it. I'm sure hacking it back would work, although to kill it you would probably have to find where it is coming out of the ground and hack it off just below the surface and repeat this process everytime it starts sending up new shoots.

I have more information about the first plant shown. It is now blooming into tall skinny shoots with teeny tiny daisy like flowers. Yellow centers, petals so fine they are almost like hairs and the petals are a pale lavender to white in color. The flowers are smaller than a dime indiameter including the petals. The centers of each flower are about as big around as a pencil eraser. Any ideas what it is?? I have it everywhere! I don't kno if the previous owner planted it intentionally or if its a noxious weed!

See if this is what you have. It ranges in color in my yard from pink/white/light lavender depending on soil conditions. Sometimes all colors are one plant.

Your photo is not clear on my monitor. Read all of the information toward the bottom. It is a very important plant.

Here is a link that might be useful: Wild aster

The first one is just a week that you can dig out.