In One Piece, Zunisha, the elephant, destroyed Jack's ship and he sank underwater. Even though he was a devil fruit eater and being stoned in sea water, he was shown being alive and waiting for reinforcements to save him. Moreover, he has sharp teeth like fish-men have. Does this mean that Jack is a fish-man?
Jack was survived in the middle of the ocean which proves of him being fish-man. However, we can't certainly say if he is a fish-man, but his ability to breathe underwater makes him so. However, despite being able to breathe underwater, he is immobile because of devil fruit. Therefore, he had to wait for reinforcements to save him.
From another SE
Yes, Jack being a fishman is the only logical explanation for him surviving in the middle of the ocean. As you noted already, he looks like a fishman too. His devil fruit prevents him from moving but that won't stop him from breathing (remember in Arlong park, Luffy could breathe while his body was under water when Nami got his head outside of the pool).
However, this is all speculation. There is not any official words about it.
We don't know.
So, first of all, Jack is either an enhanced human or a species that breathes underwater. I don't think any indication (aside from sharp teeth) has ever been given implying merman. From the wiki:
Jack is a man of massive stature
but it can be argued that 'man' just refers to 'male' in this case. Anyway, up until now (Chapter 861), no indication regarding his species has been given.
As to why he remains conscious, once more, there is no real explanation. From the wiki:
Despite being a Devil Fruit user, Jack can remain conscious underwater for an extended period of time without any visible signs of strain, aside from his inability to move; how he achieves this is not currently known.
If we consider that he belongs to a species that breathes underwater, then his inability to move is explained due to his devil powers, but he still survives (assuming someone else rescues him). However, as of this moment, we don't have any official explanation regarding this.