Learn Hardcore Japanese: doubutuen no mae de hanabi no posutaa wo mituketa. - I found a fireworks poster in front of the zoo.

動物園の前 literally means “the front of the zoo.”
花火のポスター means “poster of (or for) the fireworks.”
You see の twice because there are two separate noun-to-noun relationships in the sentence.

Why is で used after 前 in 動物園の前で instead of に?

Both に and で can mark locations, but they have different roles:

に marks a point of existence (e.g. “a cat is at the park”) or a goal of movement (“I go to the park”).
で marks the place where an action takes place.
Since 見つけた (“found”) is an action that happened there, we use 動物園の前で (“at/in front of the zoo”).

Why is を placed before 見つけた? What’s its function?

を is the direct-object marker. 見つける (“to find”) is a transitive verb, so whatever you find (here, ポスター) must be marked with を to show it’s the object of the action.

The sentence doesn’t show a subject like 私は. Who is doing the action?

Japanese often omits the subject when it’s clear from context. In everyday speech or writing, if you’re the one talking about what you did, the subject “I” (私) is understood and doesn’t need to be stated explicitly.

Why does the verb 見つけた come at the end of the sentence?

Japanese follows a Subject–Object–Verb (SOV) order. Modifiers (like 動物園の前で and 花火のポスターを) come before the verb, so 見つけた ends the sentence.

What’s the difference between the plain past 見つけた and the polite past 見つけました?

見つけた is the plain (dictionary) form, used in casual speech or writing among friends/family.
見つけました is the polite form, used in formal situations or when speaking to someone you don’t know well.
The meaning (“found”) stays the same; only the register changes.

Can I say 動物園前で instead of 動物園の前で? Is dropping の acceptable?

In very informal contexts (e.g. headlines, signboards, station names), you might see 動物園前. In everyday conversation or standard writing, you normally keep の: 動物園の前で. Omitting の in speech can sound abrupt or like a shorthand.