Learn Italian: Loro sono troppo stanchi e si rassegnano a guardare la vetta da lontano. - They are too tired and resign themselves to looking at the peak from afar.

It forms the pronominal verb rassegnarsi (to resign oneself / to yield). In Italian, this action requires a reflexive pronoun because you are resigning yourself to a situation. Since the subject is loro (they), the matching pronoun is si.

Why do we need the preposition a between rassegnano and guardare?

The verb rassegnarsi requires the preposition a when it is followed by another verb or a noun. If you want to say "to resign oneself to doing something," you must use the pattern rassegnarsi a + infinitive.

The English translation says "to looking". Why doesn't Italian use the gerund guardando here?

In Italian, any verb that immediately follows a preposition (like a, di, per) must be in the infinitive form. While English says "resign to looking," Italian strictly requires the infinitive guardare.

Is da lontano a set phrase, or could I say dalla lontana?

Da lontano is a fixed expression meaning "from afar" or "from a distance." You do not use a definite article here or change the ending of lontano, because it functions as an invariable adverbial phrase rather than a standard noun.