You would need both of them. Az az alma. - That is the apple.

There are really two different words:

1. The demonstrative az which means "that" (and always has its z), and
2. The definite article a(z) which means "the" and appears as az before a vowel and a before a consonant.

If you let one az "fall out", as you say, and write "Az alma." as a sentence, then that means "That is an apple" or possibly "That is a bunch of apples." Without any article in front of it, alma could mean an apple or a mass quantity of apples.

az = that
ez = this

a/az = the

Did the sentence change? I see ablak, not alma.

Anyway, "the one apple" could be translated as "az egyik alma".

I also would like to know how you would say ¨the one apple¨