Se tudo correr bem, hei de ver o cartaz da peça iluminado no centro da cidade.

Se tudo correr bem literally means “If everything goes (runs) well.” In Portuguese, conditional clauses introduced by se (“if”) generally use:

• the personal infinitive (correr here, because the subject tudo is explicit)
• or the present subjunctive (corra) in more formal or literary styles
  You do not use the future indicative (correrá) in an “if” clause.

hei de + infinitive is a periphrasis meaning “I shall/must.” It conveys a determined intention or mild obligation.

• hei de ver = “I shall see” (formal/resolved plan)
• vou ver = “I’m going to see” (neutral future plan)
• devo ver = “I must see” (strong obligation)

Portuguese normally uses definite articles with specific nouns:

• o cartaz (“the poster”)
• a peça (“the play”)
  If you said um cartaz or uma peça, you’d imply “a poster” or “a play,” not that specific one.

da = de + a, i.e., “of the” (feminine singular). Portuguese always contracts de + article:

• de + o = do
• de + a = da
• de + os = dos
• de + as = das
  So cartaz da peça means “poster of the play.”

In Portuguese the normal order is noun + adjective, so cartaz iluminado = “illuminated poster.” Placing an adjective before the noun (e.g., um iluminado cartaz) is possible but gives a poetic or emphatic nuance. Adjectives also agree in gender and number:

• o cartaz iluminado (masc. sing.)
• os cartazes iluminados (masc. pl.)

no = em + o (“in the,” masc. sing.). Portuguese requires the article for specific places:

• no centro = em + o centro
• na cidade = em + a cidade
  You can’t say em centro or em cidade when you mean “in the center” or “in the city.”

Yes – you get:
Se tudo correr bem, vou ver o cartaz da peça iluminado no centro da cidade.
Difference:

• vou ver is a neutral future plan (“I’m going to see”).
• hei de ver adds determination or a mild obligation (“I shall/must see”), and feels more formal or “resolved” in European Portuguese.

In hei de ver:

• hei = first-person singular present of haver
• de = preposition
• ver = main verb in the infinitive
  The structure haver de + infinitive forms a periphrastic future expressing intention or obligation, and the main verb remains in the infinitive.