Weed #2 is definitely one of the Lamiums. I'm leaning toward L. purpureum, purple deadnettle. Unfortunately, when they have become noticeable by this stage of flower color, you can kill the foliage but seeds have been formed for next year. Best time to control it is in fall when it first begins to germinate. Some of the seed usually waits until early spring, so a second application will likely be needed.
#1 looks like chickweed.
hortster

The first one is chickweed, an annual that roots at every node and that seeds prolifically.