What is the ruling regarding the phlegm that constantly afflicts me, and which I cannot expel during the daytime in Ramadan? Do I have to make up for previous days? Does it invalidate the prayer? And if it comes out, does it necessitate repeating ablution?

As for fasting: Swallowing phlegm does not invalidate the fast if it is unintentional. If one intentionally swallows it, there is no harm in following those who do not consider it to invalidate the fast, to avoid hardship and difficulty.

As for prayer: Intentionally swallowing phlegm is a matter of scholarly disagreement, and there are those who do not consider it to invalidate the prayer.

As for ablution (Wudu'): Ablution is not invalidated by expelling phlegm.

There is no evidence that indicates the desirability of rinsing the mouth after expelling phlegm. The Malikis mentioned that it is desirable to wash the mouth from any viscous substance, such as grease.