In Korean the article of the noun are not in front of the word like English. It's added at the end of the word ('ball' is one word & what follows is equivalent to the article in English). Also, it's only one ball because it didn't say how many to make after the word 'ball'. Hope that helps!
Interesting question! As a native speaker of English looking at this sentence, "Make quickly a big ball" sounds incorrect and awkward. Beside the verb "make", I only expect a noun phrase of some kind, eg. "Make me a sandwich!" or "Make a sandwich for me!" OR a preposition to turn "make" into a phrasal verb, eg "make into" = transform; "make up" = fabricate, prepare; etc. In the sample sentence, I notice that the adverb "quickly" can only go at the beginning or the end... Hope this helps to explain the issue! :-)