Learn Polish: Po co wchodzić do tych nieodkrytych ruin? - Why enter these undiscovered ruins?

It is built from the perfective verb odkryć (to discover). First, we form the passive participle odkryty (discovered), which functions like an adjective. Then, we add the prefix nie- (un-/not) to create a new adjective of state: nieodkryty (undiscovered). In this sentence, it takes the genitive plural ending -ych to agree with ruin.

Why is the word for "ruins" just ruin here? It looks like a masculine singular noun.

Ruin is actually the genitive plural form of the feminine noun ruina. As a quick refresher, most feminine nouns ending in -a form their genitive plural by dropping that -a and leaving a "zero ending". The genitive case is required here by the preposition do.

Could I use dlaczego instead of po co in this sentence?

You could, but it changes the nuance. Dlaczego asks for the cause or reason (why did this happen?), whereas po co asks for the purpose or goal (what is the point / what for?). Since the speaker is questioning the practical purpose of exploring these places, po co is much more natural.

Why is the verb wchodzić in the infinitive instead of being conjugated for a specific person?