Corn Speedwell (Veronica arvensis). They spread by seed only....pull out of the lawn as you would with Dandelions. Use a corn gluten as a pre-emergent herbicide in spring to control new seedlings.

my guess is purslane speedwell but, the I'm not sure the leaves exactly match.

For mugwort, if you find an easy, effective controlling method, patent it. Methodical soil sifting for the rhizomes (and then re-doing it for any areas that resprouts) can be practical for a small area, or a big area if you are angry/crazy enough. As far as I know, monthly mowing and controlled burns will reduce, but not eradicate it (mowing study), and hand-pulling will make it worse. Herbicides are a mixed bag, and in general are more effective if combined with mowing (reference). You may be able to avoid their use, but it will take a lot of diligence and man hours, unless someone else has a good strategy against it. Porcelain berry should be cut before flowering, since birds will disperse the seeds. If you have older ones you may have to saw it off at the base. Herbicides work, with follow-up (source). There is a possibility there are seeds in the soil already, so it may pop up again, in seemingly random places. You can pull Argeratina after a rain, and will usually get the whole root system, if you want to get rid of it. It will probably re-spread by seed into your area, eventually, if it is the wild type. Good luck!

That is torpedo grass, very tough invader. Unfortunately not many options are effective. Of course roundup works, as does pulling, but it will continue. Apparently the Florida DOT hits it with a torch, then glyphosate with good success rates. My neighbor has also had some success with Drive XLR8