Learn Turkish: Köpeğin var mı?

In Turkish, there is no direct verb for "to have". Instead, you use a structure that literally means "my [thing] exists" or "your [thing] exists". Here, köpeğin means "your dog" and var means "exists". So literally, the sentence asks "Does your dog exist?"

The dictionary word for dog is köpek. Where did the ğ come from in köpeğin?

This happens because of consonant mutation. When you add a suffix starting with a vowel (like the "your" suffix -in) to a word ending in a hard k, the k softens into a "soft g" (ğ). So, köpek + in becomes köpeğin.

What exactly does the -in at the end of köpeğin do?

It is a possessive suffix meaning "your" (when talking to one person informally). Attached to the base word for dog, it changes the meaning from just "dog" to "your dog".

Why is the question word mı instead of mi?

The yes/no question particle changes its vowel to match the last vowel of the word right before it. This is called vowel harmony. The preceding word is var, which contains the vowel a. After a or ı, the question particle is always mı.