"yok" and "değil" take some time to master. They are used interchangeably in many contexts, but not always.
yok = there isn't (something)
değil = it is not (there)
She is not home = O evde değil ~ O evde yok.
There is no bread at home = Evde ekmek yok. (Evde ekmek değil is simply WRONG)
I guess you just need to memorize as many examples as possible to get it eventually.
I do not think this is a correct sentence. Yok is not a proper verb in Turkish and this sentence does not have any verbs.
I may be incorrect but I take it that the yok is the way you know you are talking about someone or something being there or not? - Why at the pool does not exist? (no suffix for havuz indicates the use of he/she/it.) Just my understanding anyway.