i am confused brother regarding the dog's saliva as allah(swt) mentioned in the holy book that we're allowed to eat the prey which brought to us by the mouth of the hound and we aren't even asked to clean the saliva or to cut the bite of the dog on the prey.
Yes true. The killed animal in this case is going to get cleaned and cooked. High temperatures kill any and all living bacteria.
Also in surat al-kahf the story of the righteous men in the cave and their dog in accompany with them.
((And you would think them awake, while they were asleep. And We turned them to the right and to the left, while their dog stretched his forelegs at the entrance. If you had looked at them, you would have turned from them in flight and been filled by them with terror)) 18:18
The Ashabul Kahf (Companions of the Cave) were in a cave, they ran away from a corrupt society seeking the protection of Allah. And since they were living in a cave and not in a normal household environment, things which are usually prohibited in normal circumstances become permissible.
However, that is not really the case. A hunter who is required to travel a long distance to the hunting ground may require a car to get there and obviously the dog would also get a ride in the car.
With the cave, I haven't read much on the story, but if they had the dog for security, remember that they were hiding from the people/King, then obviously you would expect in such a situation the dog to go with them. The cave wasn't their home, they stopped to hide and fell asleep for 300 years.
You also had an image posted but it didn't show, I didn't see what the picture was.