Learn Hardcore Japanese: eki no esukareetaa no yoko ni mo, masukutyakuyou wo siraseru posutaa ga ikutu mo hatte aru. - Next to the station escalator as well, there are many posters stuck up telling people to wear masks.

マスクの着用
Literally: “the wearing of masks”
Slightly more explicit, a bit more neutral.
マスク着用
Drops the の and makes a tighter compound noun.
This feels more like an official notice / sign wording, similar to how English signs might say “MASK WEARING” or “MASK USE” rather than a full sentence.

Dropping の like this is common in:

Formal/official expressions
Technical/slogan-like phrases
Posters, signs, headings, etc.

So マスク着用 sounds a bit more clipped and “sign-like” than マスクの着用.

What does いくつも mean here, and how is it different from いくつか or たくさん?

いくつ = how many / how many items
いくつも (with も) = many (more than just a few), “quite a number (of)”.

In this sentence, いくつも modifies ポスター:

ポスターがいくつも貼ってある
→ there are many posters put up

Nuance compared to others:

いくつか = several, some (a smallish, unspecified number)
いくつも = many; often suggests more than you might expect
たくさん = many/a lot, neutral large quantity

Also, with negatives:

いくつもない = not many / hardly any
(literally: “there aren’t many (at all)”)

What does 貼ってある mean? How is it different from just 貼る or 貼っている?

Base verb:

貼る = to stick/paste/put up (posters, stickers, etc.)

貼ってある is the て-form + ある pattern:

貼ってある = have been put up and are (now) there
→ Focus on the resulting state (the posters are up) caused by someone’s intentional action.

Comparison:

ポスターを貼る
→ (someone) puts up posters.
ポスターが貼ってある
→ posters have been put up (by someone) and are now stuck there.
ポスターが貼っている
Grammatically possible, but for posters/signs this is usually not what people say.
〜ている focuses on an ongoing action or state; with posters we normally use 〜てある to emphasize the intentional “put-up-and-now-they-are-there” result.

So 貼ってある is a resultative form for intentional actions.

Why is it ポスターが and not ポスターは? What would change if we used は?

が here marks ポスター as the subject of existence:

ポスターがいくつも貼ってある。
→ There are many posters put up.

Using が in “Xがある / Xがいる / Xが〜てある” is the standard way to say “There is/are X”.

If you changed it to ポスターは:

ポスターはいくつも貼ってある。

This would make ポスター the topic, something like:

“As for posters, there are many put up.”

That can sound more contrastive, for example:

チラシは少ししかないが、ポスターはいくつも貼ってある。
→ “There are only a few flyers, but as for posters, there are many put up.”

In a neutral “there are ~” statement, が is the normal choice.

What exactly does 横 mean in エスカレーターの横に? How is it different from そば or 隣? Could I say エスカレーターのそばに?

横 literally means “side” or “sideways”. In location phrases:

エスカレーターの横に
→ at the side of the escalator / beside the escalator

Comparisons:

横
Emphasizes the side of something. Often “next to/beside” in a fairly physical, left-right sense.
そば
Means near / by / close to. Slightly looser; doesn’t have to be directly at the side.
- エスカレーターのそばに = near the escalator / by the escalator
隣（となり）
Emphasizes next to, adjacent, often for two discrete things side by side (e.g., two shops, two seats).
- エスカレーターの隣に could work if you imagine the posters or a board as a unit placed directly next to it.

Yes, エスカレーターのそばに is grammatically fine, just a slightly different nuance: “near/by the escalator” rather than literally “at its side”.

Is 貼ってある a passive form? There’s no “by someone” in the Japanese; how is that understood?

貼ってある is not a passive form. It’s:

貼る (transitive) → 貼って (て-form) + ある
A resultative construction: “(something) has been V-ed and is (now) in that state”

The doer (the person who put up the posters) is simply omitted, which is very common in Japanese, especially when:

The agent is obvious or unimportant (e.g., the station staff, authorities)
The focus is on the current state, not on who did it

So, in natural English, you might translate it with a passive (“posters have been put up”), but grammatically it’s not the Japanese passive; it’s the 〜てある resultative.

Is 着用 a verb here? How does it differ from just saying マスクを着ける or マスクをする?

着用 is a noun meaning “wearing (clothes, equipment, etc.)”. It’s part of the object:

マスク着用を知らせる
→ “to inform (people) about mask-wearing”

Everyday “to wear a mask” is more commonly:

マスクをする
マスクを着ける

着用 is more:

Formal / official
Used in announcements, written notices, manuals, etc.
Often appears in expressions like:
- マスク着用をお願いします。 (We request that you wear a mask.)
- ヘルメット着用義務 (Helmet-wearing is mandatory.)

So the choice of 着用 here fits the poster / public notice tone.