I think the first one is winter heliotrope. From your photo it looks the same as a plant I am still fighting with in my garden.
Only the male plant in the UK, so it only spreads in clumps, like a carpet of hell. Deep, thick beige roots, that web through the ground.
You can kill it with several doses of a Glyphosate weedkiller. Then you need to keep cutting it hard to the ground any time it pops up again to suffocate it, or apply weedkiller again. Digging it up is smart if you are irradiating a large area, but any tiny fragment will just grow again.
Whatever the name, if it is the same plant I have been dealing with, good luck.