Questions & Answers about Köpek akıllı.
Yes. You just add the question particle mı (with vowel harmony) after the adjective:
Köpek akıllı mı?
That literally asks Dog smart?, meaning “Is the dog smart?”
You have two main options:
1) Use the negative of the copula: Köpek akıllı değil. (“The dog is not smart.”)
2) Use an antonymic adjective: Köpek akılsız. (Literally “Dog mindless,” i.e. “The dog is not smart.”)
Köpek akıllı is a full sentence: “The dog is smart.”
Akıllı köpek is a noun phrase: “(a/the) smart dog.” You’d need a verb to make it a sentence, e.g. Akıllı köpek uyuyor (“The smart dog is sleeping”).
Adding -dır/-dir/-dur/-dür (with vowel harmony) makes the statement more formal or emphatic, roughly like stating a fact or general truth:
Köpek akıllıdır. (“The dog is indeed smart.”)
In everyday speech, you usually drop it and just say Köpek akıllı.