Learn Hardcore Greek: Στον δρόμο ο πεζός πρέπει να περνάει από τη διάβαση. - On the road the pedestrian must cross at the crosswalk.

Στον is a contraction of σε + τον = στον (to/in/on + the [masculine accusative]).
δρόμος is the basic (nominative) form of the noun “road”.
After the preposition σε, the noun goes into the accusative case, so δρόμος → δρόμο.

So:

σε + τον δρόμο → στον δρόμο
meaning on the road / in the street.

Why is there an article in ο πεζός, when in English we would say “a pedestrian”?

Greek uses the definite article much more than English, even when English would use “a” or no article at all.

ο πεζός literally is “the pedestrian”, but in general statements it often means “a pedestrian / pedestrians in general”.
This is common with general rules, habits, or facts:
- Ο γιατρός πρέπει να είναι προσεκτικός. = A doctor must be careful / Doctors must be careful.
- Ο άνθρωπος χρειάζεται νερό. = Humans need water.

So ο πεζός here is “the pedestrian” in a generic sense, equivalent to English “a pedestrian / any pedestrian”.

What exactly does πρέπει να mean, and how does it work grammatically?

πρέπει να expresses obligation or necessity, like “must / has to / should” in English.

Grammatically:

πρέπει does not change with person:
- Εγώ πρέπει, εσύ πρέπει, αυτός πρέπει, εμείς πρέπει, etc. (always πρέπει)
It is followed by να
- a verb in the subjunctive:
  - πρέπει να περνάει = he must cross / has to cross
  - πρέπει να φάω = I must eat
  - πρέπει να φύγουμε = we must leave

So πρέπει να περνάει is “(he) must cross”, with πρέπει να functioning much like English must / has to.

Why is it πρέπει να περνάει and not πρέπει να περάσει? What’s the difference?

The difference is one of aspect: habitual/ongoing vs one-time/complete action.

πρέπει να περνάει (present subjunctive)
- Suggests a habitual or repeated action.
- Here it means: When (he is) on the road, a pedestrian must (always) cross at the crosswalk.
- It sounds like a general rule.
πρέπει να περάσει (aorist subjunctive)
- Suggests a single, complete action: must cross (this time).
- Example: Για να φτάσει στο σπίτι, πρέπει να περάσει από τη διάβαση.
  To get home, he must cross at the crosswalk.

In your sentence, πρέπει να περνάει fits because it’s talking about what pedestrians generally should do.

Is there any difference between περνάει and περνά?

Both περνάει and περνά are correct and widely used; they are just two variants of the same form (3rd person singular of the verb περνάω / περνώ).

αυτός περνάει
αυτός περνά

Meaning: he crosses / he passes.

In this sentence, you could also say:

πρέπει να περνά από τη διάβαση

with no real change in meaning. περνάει often sounds a bit more colloquial; περνά a bit more compact/formal, but both are standard.

Why do we say από τη διάβαση and not just τη διάβαση? What does από do here?

από is a preposition that usually means from, but with verbs of motion it can also mean through / via / over / across.

With περνάω (to pass / cross), Greek normally uses από:

περνάω από τη γέφυρα = I cross the bridge (literally: I pass by/through the bridge).
περνάω από τον δρόμο = I cross the road.
περνάω από τη διάβαση = I cross at/via the crosswalk.

So από τη διάβαση shows the route or place of crossing: through / at the crosswalk.

Why is it τη διάβαση and not την διάβαση? I thought the feminine article is την in the accusative.

You’re right that the full form is την (feminine, accusative singular).
However, in modern Greek, the final -ν is often dropped before many consonants in writing and in speech.

General tendency:

Keep -ν before vowels and the consonants κ, π, τ, ξ, ψ, μπ, ντ, γκ, τσ, τζ.
It is usually dropped before other consonants, such as δ.

So:

την Ελλάδα (keep the -ν, before vowel)
την πόλη (keep, before π)
τη διάβαση (drop, before δ)

You could still see την διάβαση sometimes; it’s not wrong, but τη διάβαση is more typical modern spelling.

How do we know that διάβαση is feminine, and what does the word itself mean?

διάβαση means “crosswalk”, “pedestrian crossing”, or more generally “passage / crossing”.

Its gender is feminine, shown by:

The article η / τη(ν):
- η διάβαση (nominative)
- τη διάβαση (accusative)
The -ση ending: many Greek feminine nouns end in -ση:
- η στάση (stop)
- η σχέση (relationship)
- η πράξη (act/deed, feminine though different ending)

So η διάβαση, της διάβασης, τη διάβαση: all feminine forms.

Could the word order be Ο πεζός πρέπει να περνάει από τη διάβαση στον δρόμο? Does changing the order change the meaning?

Word order in Greek is more flexible than in English. Your alternative:

Ο πεζός πρέπει να περνάει από τη διάβαση στον δρόμο

is grammatically possible and still understandable as:

The pedestrian must cross at the crosswalk on the road.

However, the original order:

Στον δρόμο ο πεζός πρέπει να περνάει από τη διάβαση.

puts Στον δρόμο at the beginning, emphasizing the setting: On the road, the pedestrian must… (i.e., In traffic situations, this is the rule).

Changing the order doesn’t change the core meaning, but it slightly shifts what is given emphasis or what sounds more natural. The original is very natural for a general rule.

Can we drop the article and just say Στον δρόμο πεζός πρέπει να περνάει από τη διάβαση?

No, that sounds unnatural in Greek.

In Greek, subject nouns almost always take the definite article, even when they are generic:

Ο πεζός πρέπει…
Ο οδηγός πρέπει…
Ο μαθητής διαβάζει.

Dropping the article (πεζός πρέπει…) might be used only in very special, stylized, or poetic language. In normal speech and writing you should keep:

ο πεζός = the pedestrian (in general, “a/any pedestrian”).