Learn Hardcore Russian: На этой станции всегда много людей у эскалатора. - At this station there are always many people by the escalator.

So на станции is a fixed, idiomatic combination meaning at the station.
В станции sounds wrong in Russian; people simply don’t say it that way for this meaning.

What case is этой станции, and why do both words change?

Этой станции is in the prepositional case, used here after на to show location.

станция (fem., nominative singular) → станции (prepositional singular)
эта (this, feminine nominative) → этой (feminine prepositional)

In Russian, adjectives and pronouns must agree in case, gender, and number with the noun they describe.
So эта станция (this station) becomes на этой станции (at this station).

Why is it много людей and not много человека or много люди?

After quantity words like много (a lot of, much/many), Russian normally uses the genitive plural of countable nouns.

люди (people, nominative plural)
людей (people, genitive plural)

So:

много людей = a lot of people

Много человека is ungrammatical here, and много люди uses the wrong case (nominative instead of genitive).

Why is it людей and not человек after много? I thought человек can mean “people”.

Both людей and человек can refer to more than one person, but they’re used differently.

Here:

много людей = a lot of people (neutral, very common)
человек is used mainly with a specific number:
- пять человек – five people
- три человека – three people

After много, мало, несколько etc., Russian usually uses the genitive plural of a normal plural noun, so много людей is the natural form.

What case is людей, and why is that case used?

Людей is genitive plural (from люди).

The genitive plural is used because of много. In Russian, words of quantity like:

много – a lot of
мало – few/little
сколько – how many/much

usually require the genitive case, most often genitive plural for countable nouns.

So много людей literally feels like “much of people” / “a lot of people”, with of expressed by the genitive.

Why is there no word for “there is/are” like есть in this sentence?

Russian often omits есть when talking about:

general facts or habits
situations where existence is obvious

На этой станции всегда много людей у эскалатора.
Literally: At this station always many people by the escalator.

You could say есть:

На этой станции всегда есть много людей у эскалатора.

but it sounds heavier and less natural in this kind of general statement. The version without есть is what native speakers prefer here.

What does у mean in у эскалатора, and how is it different from just using a preposition like “at” or “by” in English?

У means roughly by / at / near / next to and always takes the genitive case.

у эскалатора = by/near the escalator

Typical uses:

у двери – by the door
у окна – by the window
у входа – at the entrance

There’s no exact one‑word English equivalent; depending on context it can be at, by, near, beside, etc.

What case is эскалатора, and why isn’t it эскалатор or эскалаторе?

Эскалатора is genitive singular.

Nominative: эскалатор (an escalator)
Genitive: эскалатора (of an escalator / by an escalator)

We use genitive because the preposition у always takes the genitive:

у стола – by the table
у дома – by the house
у эскалатора – by the escalator

Эскалаторе would be prepositional case (used after в, на for locations), but у never uses that form.

Could we say около эскалатора or возле эскалатора instead of у эскалатора? Is there a difference?

Yes, you can say all of these:

у эскалатора
около эскалатора
возле эскалатора

All mean roughly near the escalator, and all sound natural here.

Nuances (very slight):

у – very common, neutral, often implies quite close (right by it)
около – near/around, maybe a bit more “around that area”
возле – near, right next to, sometimes feels a bit more “close to”

In this sentence, any of them would be fine; у эскалатора is simple and typical.

Where is the subject in this sentence? What is the grammatical structure?

The core structure is:

(Есть) много людей – (There are) many people

So grammatically:

много людей is the subject phrase (a quantitative subject)
The verb есть (there is/are) is understood but not written

Full but unnatural version:

На этой станции у эскалатора всегда есть много людей.

Natural version leaves есть out:

На этой станции всегда много людей у эскалатора.

Can we move всегда or у эскалатора to other positions? For example: На этой станции у эскалатора всегда много людей?

Yes. Russian word order is flexible, and these variants are all possible:

На этой станции всегда много людей у эскалатора.
На этой станции у эскалатора всегда много людей.
У эскалатора на этой станции всегда много людей.

All are grammatical. The differences are about emphasis:

Putting на этой станции first highlights this station.
Putting у эскалатора earlier highlights the place by the escalator.
Всегда usually stands near the part it modifies (много людей), but can move a bit without changing meaning much.

Your suggested На этой станции у эскалатора всегда много людей is completely natural.

What’s the difference between много людей and многие люди?

Both involve “many people”, but they behave differently:

много людей – a quantity phrase; grammatically acts like a single unit (“a lot of people”)
- На этой станции всегда много людей.
  There are always a lot of people at this station.
многие люди – many people as a group of individuals, often followed by something about what they do/think:
- Многие люди ждут у эскалатора.
  Many people are waiting by the escalator.
- Многие люди любят путешествовать.
  Many people like to travel.

In your sentence we are talking about how crowded it is (quantity), so много людей is the natural choice.

Could we say На этой станции всегда много народа у эскалатора instead? What’s the difference between людей and народа?

Yes, that sentence is also possible:

На этой станции всегда много народа у эскалатора.

Differences:

людей – neutral, standard people; works in all registers.
народа – literally “people / folk / crowd”, often:
- a bit more colloquial
- can emphasize a crowd or mass of people

So:

много людей – many people (neutral description)
много народа – lots of people, kind of crowded, a big bunch of folks

Both are okay; много людей is the safer, more neutral learner choice.