Why can Devil Fruit users use their abilities while wet? My understanding was that the sea is supposed to weaken devil fruit users and rob them of their powers. The One Piece Wikia elaborated: 


  Devil Fruit users are susceptible to all types of water, not just seawater. This includes the white sea surrounding Skypiea. [Oda] elaborated on this, saying that "moving" water, like rain or waves, does not weaken Devil Fruit users, while standing water does.


The Wikia also states the users cannot use their powers while submerged.


  Even if a part of the user is submerged, they cannot use their Devil Fruit powers, no matter how much or how little is submerged. However, if the user's body has been permanently altered by the fruit, then the user's ability can be manipulated by outside sources (eg Luffy's neck was stretched while submerged at Arlong Park).


My questions:


How did Ajoki freeze the ocean?



May I emphasize he submerged his hand in the sea to use Ice Age?
How did Luffy fight Crocodile while wet at Marine Ford?



He was dripping wet after having fallen into the sea. Does the water not weaken him since he was now submerged? I assumed since sea stone worked just by touching it and it has the same effect as the ocean, then by having part of the ocean "touch" him would drain his power.


Are these just plot holes or am I missing something?
TL;DR 


Kuzan freezes the water without touching it. So the water doesn't nullify him. Think like how Ace tries to vaporize sea water with fire. He only creates those fire he isn't the fire in that case.
Sea water doesn't cancel Devil Fruit powers it only weakens it for the Paramecia type.




From Wikia article on Kuzan:


  In addition, Kuzan is one of the few Devil Fruit users who has adapted
  their powers to travel efficiently across the sea. In his case,
  freezes the water underneath Ao Chari then rides across the sea, due
  to the water freezing as the wheels pass over it. This freezing
  ability, which can be used on a very large scale, renders Kuzan one of
  the few Devil Fruit users who can actually counteract the weakness of
  falling into a large body of water and drowning, as he can just freeze
  the water and stand on the ice.


From the Wikia article on Logia


  Logia Devil Fruits allow a person to create, control, and transform
  into a natural element or force of nature, depending on the fruit. The
  user can transform partly, or completely.




For Luffy's case, check this post.