На этом перекрёстке нельзя обгонять.

Russian uses different prepositions for location depending on how a place is conceptualized.

• на + Prepositional is common for open areas / surfaces / “sites” like на улице (on the street), на площади (in the square), на мосту (on the bridge), and also на перекрёстке (at the intersection).
• в + Prepositional is more for enclosed spaces (in a room, in a building, etc.).
  So на этом перекрёстке is the standard, natural choice for “at this intersection.”

It’s Prepositional case (also called “locative” in some contexts), triggered by the preposition на when it means location.

• этот перекрёсток (Nominative)
• на этом перекрёстке (Prepositional)
  You can recognize Prepositional here by этом and the ending -е in перекрёстке.

Because adjectives/pronouns agree with the noun in case, number, and gender.

• перекрёсток is masculine singular.
• After на (location), it needs Prepositional.
  So этот → этом to match перекрёстке.

нельзя is an impersonal predicative word meaning “it’s not allowed / it’s impossible / one must not,” depending on context. It often introduces a general rule and doesn’t have a subject.
Pattern: нельзя + infinitive
So нельзя обгонять = “(it is) forbidden to overtake.”

Because нельзя typically combines with an infinitive to express prohibition in a general, impersonal way. There’s no explicit “you/we/they” subject.
If you wanted a direct command to a person, you could use an imperative instead (different style): Не обгоняйте! = “Don’t overtake!”

With rules and prohibitions, Russian usually uses the imperfective infinitive to mean “not allowed to do this in general / at any time here.”

• нельзя обгонять = “overtaking is not allowed (as an activity here).”
  нельзя обогнать is possible in some contexts but tends to sound more like “it’s impossible / you can’t manage to overtake (successfully)” or a more specific one-time situation, not a general rule on a road sign.

It strongly sounds like a rule/sign/instruction (traffic context). The structure На … нельзя + infinitive is very common for posted rules:

• Здесь нельзя парковаться (Parking is not allowed here)
• Входить нельзя (Do not enter)

Yes, that’s grammatical. Differences are mainly stylistic:

• нельзя обгонять is shorter and very natural for signs and spoken warnings.
• не разрешается обгонять is more formal/official (“is not permitted”).
  Meaning is essentially the same here.

The stress is: перекрЁстке.
The letter ё is always stressed in standard Russian, and it’s pronounced yo (like yoh). In many texts ё is often written as е, but pronunciation remains ё: you may see перекрестке written, but it’s still pronounced перекрёстке.

Yes. Russian word order is flexible and changes emphasis:

• На этом перекрёстке нельзя обгонять. Neutral: “At this intersection, overtaking is not allowed.”
• Обгонять на этом перекрёстке нельзя. Emphasizes обгонять (“Overtaking—at this intersection—is not allowed.”)
  Both are correct; the first is more typical as a sign-like statement.