When Freddy discovers Jason's weakness to water, he adds insult to injury by showing the dismembered head of Jason's Mother in front of his child form. Now Jason is a Genius Bruiser when it comes to killing, everything else however he is not so smart. So when he sees his mother's head he comes to the logical conclusion (in his point of view.) that Freddy killed Mrs. Voorhees. When Freddy enters the real world, Jason even stops going after the others just to confront Freddy.
Freddy's strange bout of Off Screen Teleportation could be explained by him running like hell and scampering up the platform while Jason is taking his time to stand back up after the torpedo strike.
Rather a subtle one at the start with Freddy. Krueger is in Hell, and (theoretically) suffering the torments of the damned. What do we see of his 'torment'? Freddy surrounded by pictures of all the children he murdered, while being unable to kill any more. That is Freddy Krueger's Hell. Knowing that he killed dozens of children... And can't kill more of them. He's THAT evil.
Jason's version of Hell is in Camp Crystal Lake. He's killing teenagers. They're all very bad. But no matter how many he kills, they won't die. They keep coming back and he can't finish the job.