"diye" is a particle [Originally an adverb derived from the verb "demek" ]

can mean ;

1. "called","named"

Geçen yaz Alaçatı diye bir yere gittim.

I went a place called ´Alaçatı´ last year.

2. ´in order to ´, ´so that´

Doktor olasın diye seni tıp fakültesine gönderdim.

I sent you the medical school in order to become a doctor.

I sent you the medical school so that you become a doctor.

3. ´in case´

Yanlış yöne dönersin diye senin yanında oturuyorum.

I am sitting beside you in case you might turn the wrong direction.

Thanks for adding your answers. I am also a learner, but I hope I can explain your errors to help you.

10] kitaplıkta = on/in/at the bookcase

Kitaplıkta dört kitap var = There are 4 books in the bookcase.

kitaplıktan = from the bookcase

Kitaplıktan bir kitabı seçtim = I selected a book from the bookcase.

11) Siz dün tiyatro .... git...... ?

If we see the subject is siz, then the verb at the end must agree with the subject. So it has to be gittiniz mi ?

I guess you know the rule that when a suffix starts with a vowel, it needs a buffer letter to join a word ending with a vowel

tiyatro + a/e (to the theatre)

= tiyatro+y (buffer letter) + a (for vowel harmony)

= tiyatroya (to the theatre)

Siz dün tiyatroya gittiniz mi? (Yesterday, did you go to the theatre?)

12) Yemekler güzel miydi? (Was the food nice?)

which is different to .....Yemekler güzel mi? (Is the food nice?)

Evet harika.....

The question indicates past tense of the old Turkish verb for ´to be´. (imek)

imek (not used these days) = to be

idi = it was

so the answer must also say ´it was´ (idi)

harika + idi (needs a buffer, so the i mutates to a y) to become

harika + ydı = harikaydı = it was fantastic

hasta (sick), hastayım (i am sick), hastaydım (I was sick)

see more explanations here

The same happens for the with suffix (ile)

Araba + ile = arabayla (by car, with a car)