Hello. It means the following: Akzhan used to study in city. So, now she doesn`t study there. And "оқитын" is not short form of "оқып тұрады". You can say like these: Ақжан анда-санда кітап оқып тұрады = Akzhan sometimes read books. But you can say like these: Ақжан анда-санда кітап оқып тұратын = Akzhan used to read books sometimes.

Ақжан қалада оқитын. Akzhan studied in city. 'оқитын' is past simple. 'оқып турады' is future simple. E.g. Akzhan will be study in city.