Most likely this is Broussonetia. Second option is Morus alba (same family, Moraceae). Both have very variable shape of leaves, even on the same branch differently looking leaves can be found. Here is a link that might be useful: Broussonetia

Discoqueen - it's an elder bush. Sambucus nigra - a very common self sowing native. You will need to cut it right down and then, if you can't dig out the roots, apply some sort of brush killer to the stumps. Before anyone says, why destroy an edible, these things are native here and sprout all over the place. They are a bit too common and a bit too large to tolerate in our small gardens.

I think it's one of the dayflowers; if it is, you should be seeing a blue flower any time now. Most herbicides don't work on dayflowers, which leaves hand-pulling; in my experience (& I've been fighting dayflower for years), it's much easier to pull when the ground is moist, as the stem will just break off and leave the roots if the ground is dry. Here's the Wikipedia page on the dayflower family: https://en.wikipedia.org/wiki/Commelinaceae; if you can track down some close up pictures as good as the one you posted, maybe you can firm up the dayflower diagnosis.

Dallisgrass. MSMA for existing weeds and prodiamine to prevent new seeds from sprouting. Keep lawn short to prevent seed heads from forming. Spreads quickly if left unchecked.