"Airports are big."
I'm just surprised they're mixing informal conjugations in with formal, while I thought formal was moreso taught first as it's generally the best way to start out communicating.
That's actually quite debatable, there's some good reasons to do it the other way. Also, one of the common humorous observations about foreigners speaking Japanese is that often end sounding overly formal and / or feminine.
It all depends on why you're learning and what you wanna use it for. I don't wanna write an essay or give a speach, all I want is to understand what I hear on animes (because we all know what happens during translations: shenanigans). So when I finally found out here on the comments (and only recently in the lessons) that ではありません was the same as じゃない I was like ohhhh ok, now we're talking. As much as I see it's important to know those extra polite forms, I don't see myself ever using them. It's just like studying english and learning to say "hello, how are you?" but what you actually say is "hey, what's up?" (not to go with "yooo wusup" :P)
You don't need a copula for i-adjectives, technically. You actually don't need a copula at all a lot of the time. です generally just adds politeness.
Somewhat belated, but Japanese has two-types of adjectives: i-adjectives and na-adjectives.
The i-adjectives all end in い, and have the same form whether before or after the noun (i.e. 古い車です(/車は古いです). The na-adjectives can end with anything (including い, as in きれい), and they gain a な when placed before the noun (i.e. 有名な人です/人は有名です). The two kinds of adjectives also conjugate differently.
A copula is a kind of verb used to join an adjective or noun to a subject. In English, "to be" is a copula: I can say Fred is tall (an adjective) or Fred is a plumber (a noun). です serves a similar purpose in Japanese. In English, copulas are only skipped in very colloquial speech (e.g. "[Are] you from out of town?"), but Japanese is a bit more permissive about it.
When I'm asked to translate: "Airports are big", shouldn't は be replaced by が?
I mean, that could work, but wouldn't sound natural as you almost never use が for simple sentences with です unless the shnanigans happen where は and が switch places. Oh yeah, they do that sometimes.