I am trying to read a children's book and I am stuck on the first line

Okullar tatil oladı yaklaşık bir ay olmuştu.

I think this means something like "The school holidays were approaching and just one month away" but I cannot understand some of the words.

Okullar tatil - school holiday
oladı - bu anlamadım
bir ay - one month
ol-muş-tu - it is said that it will become
why is the -muş- tense used here instead of oldu?

yaklaş-ık - I assume this is the verb stem for yaklaşmak meaning "to approach" (I hope it is not the other meaning of this verb as this is a book for 2 year olds ). I can work out that the -ik suffix is a deverbal substansive suffix but what does it deverbalise yaklaş into?

"yaklaşık" means "approximately".
I can translate the sentence but I'll leave the explanation to the experts:

Since the school vacation had started it's been approximately one month.

olalı = since it was

For example the song of Sezen Aksu:

İstanbul, İstanbul olalı
Hiç görmedi böyle keder.

(Ever) since İstanbul is İstanbul
She has not seen such sorrowç


I am not sure though, if in other cases than the verb 'to be', it needs a repition. For example.. 'Gitti gideli' or just 'gideli'. I am confused because I have heard 'Gitti gideli' used..