Does Kaido possess any other power other than just being physically strong? Kaido (カイドウ) has such incredible strength. But, to be one of the Yonko, it takes strength beyond even an Admiral level and there must be an explanation for Kaido. The most normal person I've known as Yonko is Shanks, but since he possesses incredible and powerfull Haki so it makes sense. But Kaido? Does he have mysterious power other than just being physically strong?

From One Piece Wikia :


  Perhaps the greatest sign of Kaido's strength is his apparent
  inability to die. He has been caught and tortured 18 times, and people
  as powerful as the Marines and other Yonko have attempted to execute
  him 40 times. However, he mysteriously survived every single attempt
  because every single execution weapon broke when being used on him.
  Most notably, Kaido has jumped from 10,000 meters in the sky onto the
  ground, creating a massive shockwave strong enough to sink a large
  ship nearby, and emerged without an injury; it has even become a hobby
  for him to attempt suicide, only for it to fail.


That's not enough explaination about Kaido's power.

Here is the thing, you know Admiral Akainu (赤犬),  possesses the Magu Magu no Mi which grants him the ability to transform his body into terrifying magma and manipulate it at will, he can even afford to crush a land if he wants. But hey, that's not enough to match a Yonko.

So back again to Kaido, Does he have any other mysterious power?
All these information that you've posted are detailed and relevant to what had been released in the manga and also what has been shown in the anime.
Currently the manga is in an arc which is focusing on something else. If you would like to know, you can read from the manga.

SPOILERS


   Currently due to the Sanji situation, in the manga, it will focus on the development of Big Mom's character and the adventures to be on whole cake island. As we know from the impel down arc and marineford arc when the crew splits up the story will follow Luffy as he is the protagonist. Zoro and the others have split to Wano and are likely to engage Kaido first. So just stay tuned and your question should be answered sooner than you know it.