From what I've heard from native speakers of Turkish, the sound of the letter E does shift to a short A sound in certain words (especially in words ending in 'ler'). Best course of action, when writing, is to make sure the vowels match. 'ler' goes after a final vowel of e i ö or ü and 'lar' goes after a final vowel of a ı o or u.
When that is strange. I read everywjere that Turkish is supposed to be phonetic as you say but as people here are saying, the 'e' before /m, n,l, s,z/ does normally sound more like æ to me.
On top of that, I've a Turkish friend called Ekrem who normally explains that his name should be pronounced more like Ekræm. So I 'm confussed about this.
The Turkish alphabet is more phonemic than phonetic. That's to say if a difference in pronunciation affects meaning, it's reflected in writing, but other variance isn't reflected. [æ] is how the letter e is pronounced in those environments you mentioned, but it never contrasts with [e], so it's contained under the umbrella of the letter e.
Is there a reason why greetings/farewells use the plural forms of nouns? For example, "geceler" is the plural for "gece," which means night, correct?