Yes, those are definitely wild violets and you are in for a fight to get rid of them. I had them invade my lawn this year and after fighting them since spring I gave in and used Roundup on the entire yard. I started out using triclopyr which put a really big dent in them however that will kill out your bermuda. Not really sure what will work. Metsulfuron is what they recommend for wild violets in bermuda but I have no experience with that.

That's mayapple, Podophyllum peltatum. Most woodland gardeners would consider it a wildflower. Has a rather large white flower, in mid-May, which kind of hides beneath the leaves. Has a spreading root system. Will turn yellow and die back to the ground by August, at least here in New Jersey. Never heard of anyone wanting to control it, but I guess you could just mow over it.

Top right is prostrate spurge (which pull immediately before seeds disperse), middle right side is wood sorrel and the ugly red and white in the center is a stinkhorn mushroom. Might be nutgrass on the left - does it have a triangular stem? hortster

I do not know the name but I have some of the same weed. I sodded a portion of my front lawn this past spring with St Augustine Palmetto. I have hand removed a dozen or so pieces of this stuff in the new sod. Never saw it before the new sod.