Translation:I saw the Hagia Sophia for the first time when I was fifteen.
Kez and kere have same meaning and We use kere and kez,when we want to say repeated action. For example "Oraya 2 kez/kere gittim." (I went there twice) "Zaman" and "Vakit" are different from kere and kez and "zaman/vakit" have same meaning and we use generally them simple. "Ne zaman/vakit geleceksin?" (When will you come" "Zaman/Vakit geldi mi?" (Did The time come)
No, that sounds very clumsy. Try and always say "ilk kez + time expression".
Ayasofya'yı ilk kez 2005'te gördüm.
Ayasofya'yı ilk kez üniversitede(yken) gördüm.
Ayasofya'yı ilk kez evlenince gördüm.
and so on.
Alternatively, you can "relative clause"-ify the "gördüm"-part of the sentence:
Ayasofya'yı ilk kez gördüğümde on beş yaşındaydım. = When I first saw Hagia Sophia, I was 15 years old.
And by the way the "kez" is omittable in all of these sentences.
Is Ben a person? (Like Ben Affleck?) Otherwise, it's öğrendim*
Both are correct. They just stress different things:
Ben onun dün oraya niye gelmediğini Alan'dan öğrendim.
→ It's from Alan (and not from Ektoras) that I learnt why s/he didn't show up there yesterday.
Here's how I say this sentence: http://vocaroo.com/i/s0IbIM32Mrem
Ben Alan'dan onun dün oraya niye gelmediğini öğrendim.
→ What I learnt from Alan was (not what his or her name was, but rather) why s/he didn't show up there yesterday.
Here's how I say this sentence: http://vocaroo.com/i/s1sfexN5h3ze
P.S. I've assumed in both sentences that I learnt from Alan why some specific person (other than Alan himself) didn't show up there yesterday.