أل here is like the article ''the'' in English. ''the'' is used to refer to specific or particular nouns and the same things for أل let's read the book هيا لنقرأ الكتاب.....في هذه الجملة أنا أعني كتاباً محدداً while a/an in English is used for the non-specific or non-particular nouns. Let's read a book هيا لنقرأ كتاباً ... في هذه الجملة أعني أي كتاب وليس كتاباً محدداً And as Ahmed said the Tanween (ً ٌ ٍ ) in Arabic in general is used for the non-specific or non-particular nouns. so regarding to your sentence كنتُ أعمل في مقهىً he said مقهىً with Tanween..... that means he doesn't want to specify . it's like : I used to work in ((a)) cafe أنا الآن أعمل في مدرسةٍ ثانويّةٍ I work now in ((a)) high school. If you want to specify, you are going to say كنت أعمل في (الــ)مقهى ، وأنا الآن أعمل في (الــ)مدرسةِ (الــ)ثانويةِ

it's just as in English or another language .. when you say The school , so we know witch school but a school , we don't know witch school , this is why using ثانوية and not الثانوية

You should say " أنا أعملُ في مدرسةٍ للمرحلة الثانوية" because i think if you just say " أنا أعملُ في مدرسة ثانوية " it means like i am working in a Minor school not a main school. But if you said " أنا أعملُ في مدرسة للمرحلة الثانوية" it is mean like i am working in a school for the secondary stage. I hope i explaned something :)

It is as in English language : name without (ال)= (a or an)+name=name unknown for you name with (ال)=the + name= known for you If someone said: I saw (a) school (مدرسة)= as a listener, I do not know which one ( unknown for me) . but if the speaker continued his speaking for example: the school (المدرسة) where am studying in. in this case it known for me . I wish you got me.

اضافة حرفى " ال " الى كلمة تعنى تحديد شىء او مكان معين معروف لمن اتحدث اليه لكن كتابة الكملة مجردة من حرفى " ال " فهى هنا كلمة عامة , لا اقصد مدرسة بعينها