Why not hayvani here? Should "the fastest animal" not be in accusative?
It is not a direct object, so no :) This is a predicate nominative (just like the sentence "The student is a painter." There is no direct object here).
Can I put 'kesinlikle' on the first place: Kesinlikle aslan en hızlı hayvan?
Not here, it would sound a bit odd. (Consequently, "Definitely the lion is the fastest animal" also sounds a bit odd)
I am sure Puma is faster than it
What's the difference between hızlı and çabuk?