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.
It is heavily implied that Freddy killed Jason to begin with. If Freddy was murdered by the parents of Elm Street before their children were born...then that would make the date of Freddy's death at somewhere around 1970. Jason died in 1957. In other words...Freddy murdered children for at least 13 years.