The white flower is a native woodland plant, Circaea alpina, commonly called enchanter's nightshade. I’ll note that it isn’t in the same plant family as bittersweet nightshade (Solanum dulcamara) or deadly nightshade (Atropa belladonna) so I’m sorry for this little plant getting the common name it has. Here is more information about this little wildflower, with more here. I don’t see any listing for it being rare or endangered.
When it appeared in my garden I quickly realized it was expanding more than I wanted, and has a dormant season when I wanted a showy late-season plant. I used a hoe and kept all the green cut off. Deep woodchip mulch also helped me keep seeds in the dark, limiting sprouting.
The second plant is Mentha requienii, or Corsican mint. I buy it at plant nurseries to keep it as a strong groundcover in my landscape because the scent makes me nostalgic for my grandmother’s garden in my childhood. It spreads as branches root and from seed, which is why it pops up where you don’t want it.
Both of these grow in moist areas, so keeping it dry is one method is discourage their growth.
They both expand under(or above) ground in addition to spreading by seed. Persistent removal of leaves will eventually exhaust energy in roots and kill the plants, while also stopping flowers from making more seeds. I find a hula hoe, also called a stirrup hoe, works well for slicing the tops off patches of plants just below the surface. Check for green growth weekly to begin your attack, and don’t forget to start again in early spring next year. Smothering with a thick coat of wood chips helps in addition to hoeing.
Broadleaf herbicide, applied following label instructions is an option. If you’d like more information on that option, let us know.