Learn Turkish: Dünkü hayal sadece geçmiş. - Yesterday's dream is just the past.

The adjective-forming suffix -ki is special because it usually ignores vowel harmony, staying as -ki even after back vowels (like in yarınki - tomorrow's). However, there are a few exceptions! When added to the words dün (yesterday), bugün (today), and gün (day), it changes to -kü to match their rounded vowels.

Does hayal mean the kind of dream you have while sleeping?

No, hayal means "dream" in the sense of a daydream, your imagination, or a hope for the future. If you want to talk about the visual dreams you have while asleep in bed, you should use the word rüya.

I learned that -miş is a past tense verb suffix. Is geçmiş a verb here?

In this sentence, geçmiş is acting as a noun meaning "the past". It does come from the verb geçmek (to pass) combined with the -miş suffix, literally meaning "that which has passed". It is very commonly used as a noun, just like its opposite gelecek (the future), which comes from gelmek (to come).

Where is the verb in this sentence?