I am reviewing my lessons and want to make sure I understand this. Please correct me if I am wrong.

The door of the house. Evin kapısı.

But if I was pointing to the house and said, "The door of this": Bunun kapısı.

And a question: Şunun and şunların are used in situations where the object is not right here but is not way down the road, either, yes? Is that what is meant by "between this and that" and "between these and those"?

Likewise: Şu and şunlar?

One more question, on a different topic:

Senin kitabın, yes?

But one of the correct answers on a test here is: Senin kitabin.

Am I misunderstanding the vowel harmony rule here?

But please be aware there are the odd exceptions to the vowel harmony rule, (as I understand because of a slightly different pronounciation)

kalp (heart) becomes kalbim (my heart)

saat (hour, clock) becomes saatler (hours, clocks)

meşgul (busy) becomes meşgulüm (I´m busy)

Two more grammar questions:

Please explain this kind of construction: "Kuşlar, ´merhaba´ dedi." "Berk, uyandı." Is the comma here just for emphasis? These sentences would also work without the comma, wouldn´t they?

And in that first sentence, about the birds, the verb is not dediler because we have "lar" on the noun and don´t want to repeat it? 

Teşekkürler!

Yes, in my opinion the comma has only been used here for effect. Generally, in my textbooks, spoken speech is in within inverted commas, and starts with a capital letter. (when you use dedi). If the subject is not specified or obvious, then the plural ending is used. If the subject has been pluralised (is that a word?), then Turks are generally economic with words, and the plural suffix is dropped from the verb.

An example of where a comma, or lack of, can change a meaning

Babam bana "Oku, baban gibi, esek olma" dedi.

(My father said to me "study, like your father, don´t become a donkey".

Babam bana "Oku, baban gibi esek olma" dedi.

(My father said to me "study, don´t become a donkey like your father".