>>6570351: Use mulch and/or landscaping cloth under the rocks. Plant other ground cover.
2: Looks like Chickweed (Stellaria media). It sprouts and grows best in the cooler months. It is edible and delicious. It has saponins in it so if you use it as a pot herb it can make the water appear sudsy, but don't worry about it. Just don't consume massive quantities of it. Sometimes as a salad green you can taste a hint of soap because of the saponins.
Wait for it to flower and seed. You can tap it and brush its seeds into a container or pick a bunch and shake into a container. It will grow readily. I have a big vial of seeds for my garden. I grow it for ground cover in my garden and as food.
This is what it looks like when it blooms. The leaves on these flowering sections will be more lance-shaped than the ones that look more like a spade-shape when not flowering.