Learn Portuguese (Portugal): Eu olharei para aquela estrela.

To form the future tense for regular verbs like olhar, you simply take the full infinitive verb (olhar) and add the future endings. For eu (I), the ending is -ei, which gives us olharei (I will look).

Why do we use para here when the English translation says "look at"?

In English, we say "look at", but in Portuguese, the verb olhar pairs with the preposition para when you are directing your gaze toward something. So, olhar para translates to "to look at" or "to look towards".

Why does the sentence use aquela instead of essa for "that"?

Both essa and aquela mean "that", but they imply different distances. Aquela is used for things that are far away from both the speaker and the person being spoken to. Since a star (estrela) is very far away, aquela is the natural choice.

Is the word eu strictly necessary in this sentence?

No, it is optional. The ending -ei in olharei already makes it perfectly clear that the subject is eu (I). You can just say Olharei para aquela estrela, but keeping eu is totally fine and adds a slight emphasis.