Learn Hardcore Portuguese (Portugal): Não atravesses a rua fora da passadeira. - Don’t cross the street outside the crosswalk.

Because negative commands in Portuguese use the present subjunctive. For tu (informal singular), the present subjunctive of atravessar is tu atravesses, so the command is Não atravesses.... In the affirmative, tu commands are built from the present indicative minus the final -s: Atravessa a rua... (not negative).

Present indicative (tu): tu atravessas
Affirmative imperative (tu): Atravessa
Negative imperative (tu): Não atravesses

How would I say this formally or to more than one person?

To one person formally/distantly (or in signs): Não atravesse a rua fora da passadeira. (addressed to você or o/a senhor/a)
To several people: Não atravessem a rua fora da passadeira.
“Let’s not cross …” (inclusive): Não atravessemos a rua fora da passadeira.

Subject pronouns are usually dropped: the forms themselves show who is meant.

Can I say Não atravessa a rua...?

Not in European Portuguese when giving a command to tu. Não atravessa is the present indicative (he/she/you-você doesn’t cross) and doesn’t function as a negative imperative in EP. Use:

Não atravesses (tu)
Não atravesse (você)

In Brazil, you may hear Não atravessa as an informal command to você, but in Portugal it’s not the standard.

What exactly is passadeira in Portugal? Are there other words?

In Portugal, passadeira is a pedestrian crossing, often a zebra crossing. You may also hear:

passadeira de peões (more explicit: “pedestrians’ crossing”)
passagem para peões (formal/administrative) Brazilian Portuguese uses faixa de pedestres. Note that passadeira can also mean a long narrow rug or a treadmill, but context makes the meaning clear.

Why fora da passadeira and not fora de passadeira or fora a passadeira?

The pattern is fora de + noun (“outside of …”). Portuguese normally uses articles with singular count nouns, so you get fora de + a passadeira. The preposition and article contract: de + a → da, hence fora da passadeira. Bare fora de appears in set expressions (e.g., fora de horas) or with abstract nouns.

Why a rua and not à rua or just rua?

It’s a direct object, so there’s no preposition. Use the simple definite article: a rua.
à is the contraction of a + a (to the + feminine), used with a preposition (e.g., Vou à rua = “I’m going out to the street”).
Portuguese normally requires an article with singular count nouns, and street names also usually take the article in Portugal (e.g., na Rua Augusta).

When would I use rua instead of estrada?

rua = street (typically urban)
estrada = road (often interurban/rural) You could say Não atravesses a estrada fora da passadeira, but crosswalks are more typical in urban areas, so rua is the more usual word here.

How do you pronounce the sentence in European Portuguese?

A quick guide:

Não: nasal ão (similar to English “own” but nasalized).
atravesses: stress on -ves-; final -s sounds like “sh” [ʃ]; the ss between vowels is a clear [s].
a rua: initial r is guttural [ʁ] in EP; two syllables: ru-a.
fora: stress on fo-; the r here is a tap [ɾ].
da: reduced vowel [ɐ].
passadeira: stress on -dei-; ei ≈ “ay” in “say”; the r is a tap [ɾ].

Approximate IPA (EP): [nɐ̃w ɐ.tɾɐˈvɛ.sɨʃ ɐ ˈʁu.ɐ ˈfɔ.ɾɐ dɐ pɐ.sɐˈdej.ɾɐ]

Can I move fora da passadeira or omit a rua?

Yes:

Fronting for emphasis: Fora da passadeira, não atravesses a rua.
Omit the obvious object: Não atravesses fora da passadeira. The original order (Não atravesses a rua fora da passadeira) is the most neutral.

How do I say the same idea positively?

Several natural options:

Atravessa a rua na passadeira.
Só atravessa na passadeira.
Atravessa a rua apenas na passadeira.
On signs: É favor atravessar na passadeira. or Atravessar só na passadeira.

Where do object pronouns go in a negative command?

With negation, clitic pronouns go before the verb (proclisis):

Não a atravesses fora da passadeira. = “Don’t cross it (the street) outside the crosswalk.” In affirmative commands, they attach after the verb (enclisis), often avoided in speech if it sounds clunky:
Atravessa-a na passadeira. (perfectly correct, but many speakers rephrase to avoid the hyphenated ending)

What mood/tense is atravesses, and what are the key forms I should know?

Atravesses is present subjunctive. Relevant forms:

Present subjunctive: eu atravesse, tu atravesses, ele/ela/você atravesse, nós atravessemos, vós atravesseis, eles/elas/vocês atravessem
Present indicative (for contrast): eu atravesso, tu atravessas, ele/ela/você atravessa, nós atravessamos, vós atravessais, eles/elas/vocês atravessam
Imperatives (EP):
- Affirmative tu: from indicative without final -s → Atravessa
- Negative tu: present subjunctive → Não atravesses
- você/vocês (both affirmative and negative): present subjunctive → (Não) atravesse/atravessem

Is atravessar the only natural verb here? What about cruzar or passar?

Use atravessar to mean “cross (from one side to the other)” a street/road. In Portugal:

cruzar is more often “to cross/meet” in the sense of paths crossing or “to run into” someone (cruzar com alguém).
passar (a rua/estrada) is less idiomatic for crossing from one side to the other; prefer atravessar. You can say passar pela passadeira (“go via the crosswalk”), but for the act of crossing the street, atravessar (a rua) na passadeira is the standard.

What’s with the double ss in atravesses and passadeira?

Between vowels, a single s sounds like [z] in Portuguese. To keep the [s] sound, you write ss:

casa = [ˈkazɐ] (z sound)
caça = [ˈkasɐ] (s sound) Hence atra-ve-ss-es and pa-ssa-dei-ra use ss to ensure [s].