I bambini giocano a pallone nel cortile finché non fa buio.

• In Italian, the verb giocare takes the preposition a before the name of a sport or game: giocare a calcio, giocare a tennis, giocare a pallone.
• These are fixed expressions, so you don’t add an article.
• Saying giocano con un pallone would literally mean “they play with a ball” in a general sense (tossing or kicking any ball), not “they play soccer.”

• giocare con la palla means “to play with the ball” (e.g. rolling, throwing, catching it).
• It’s not used to indicate the sport of soccer; for that you always say giocare a pallone.

• pallone is a large ball (e.g. a soccer ball).
• palla is a smaller ball (e.g. tennis ball, beach ball, kids’ bouncy ball).
• The idiom giocare a pallone specifically evokes the traditional “playing soccer/ball” scene in Italian culture.

• nel cortile is the contraction of in + il and refers to a specific courtyard.
• You can also hear in cortile, which speaks of “the courtyard” in a more general or habitual sense.
• al cortile is incorrect here: location inside an enclosed space uses in, not a.

• In Italian, finché non (= “until”) is a set phrase; the non is not negating fa buio, it’s part of the conjunction.
• You always pair finché with non when marking the end-point of an action: finché non torna (“until he returns”), finché non smette (“until it stops”).

• Yes. Both fino a quando non fa buio and fino a che non fa buio mean exactly the same as finché non fa buio.
• finché is more concise; fino a quando/​fino a che are slightly more formal or emphatic.
• In everyday speech you may also hear people drop the non after quando, but prescriptively it stays.

• The impersonal verb fare is common to express weather or ambient changes: fa caldo, fa freddo, fa buio (it gets dark).
• You can say diventa buio (“it becomes dark”), which is correct but less idiomatic.
• si fa buio is quite rare; the standard expression is simply fa buio.