Does swallowing saliva mixed with saliva collected outside the mouth invalidate the fast, especially given that it did not completely exit? And does the ruling of a small amount of food mixed with saliva, which is permissible to swallow, apply to it?

The fast is invalidated if a fasting person intentionally swallows some saliva that has come out of his mouth onto his clothes, hand, or the outer part of his lips. However, if he swallows saliva unintentionally, or has doubts about it, his fast is valid. Saliva that comes out of the mouth is different from a small amount of food that is difficult to guard against; the latter does not break the fast unless it was possible to guard against it and he failed to do so. It is advised to beware of obsessive thoughts (waswas) and to treat them by ignoring them.