Does the emission of some light saliva onto a mask while speaking, and its re-entry into the mouth, break one's fast? And does it break one's fast if it dries on the lip and then the lips are closed?

If saliva reaches the lips and a person unintentionally swallows it, then there is no blame on him. If saliva dries on the lips and then he closes them, he does not break his fast. However, if he intentionally swallows it after it has reached the lips, there is a difference of opinion:

The Shafiis and Hanbalis: They hold that it invalidates the fast because it has separated from its original place inside the mouth, similar to swallowing anything else that has separated. The Hanafis: They hold that it does not break the fast unless the saliva completely separates from the mouth and then he returns it and takes it back in.

It is preferable to refrain from intentionally returning saliva that has separated from outside the mouth back inside. What enters unintentionally or what is difficult to guard against is excused. And if its re-entry is not certain, it does not break the fast, for the default is non-invalidating.