Learn Portuguese (Portugal): Eu hei de enfrentar este problema e superar o medo. - I will face this problem and overcome fear.

Using the haver de + infinitive structure expresses a very strong personal determination, conviction, or promise. While vou enfrentar simply states a future plan, hei de enfrentar sounds more like I am determined to face or I shall face.

I am used to seeing haver as há (there is). Where does the word hei come from?

Hei is the eu conjugation of the verb haver in the present tense. While you often see it frozen as há (there is/are) when talking about existence, when we use haver de to express intention, we fully conjugate haver to match the subject.

Does the hei de also apply to superar later in the sentence?

Yes! Because the two actions are joined by e (and) and share the same subject, the auxiliary hei de carries over to the second verb. You are essentially saying Eu hei de enfrentar... e (hei de) superar. Leaving it out the second time sounds much more natural.

Why do we need the article o before medo if the English translation is just fear?