Birch sap is used fir making birch beer and strawberry water sounds like it would work just as lemon does for the skin but orpiment (a toxic mineral that contains arsenic) and (::gulp::) frog-spawn water just sound crazy to me.
This receipt is not referring to real worms, but clogged pores. Before the common access to microscopes, many people believed that the oil blockage of a pore was a worm. This believe was still present as late as the American Civil War when magazines were quick to point out that "ignorant persons" still believed it.
Even today some people swear by the whites of eggs to remove blackheads and using the plant Soloman's Seal (Polygonatum) to cure acne.

In some places, especially at the beginning of the 1700s, it was common for people to share bowls and cups at the table. Dishes were not washed with soap, even in taverns where many people could have used the same cup all day.
*Note: The baby in the picture at the top is wearing a "pudding cap" which protected the heads of children while they were learning to walk.