The reason Joker was able to resist Hal-Spectre's mindrape was because it happened at the time of Joker's Last Laugh (that's the name of a story arc) when his mind became more powerful as a result of being psychically connected to the Jokerized characters. In Joker's Last Laugh, Joker thought he was dying (although later this was disproven) so he started jokerizing most of the super villain community which he became psychically connected to.
And Corrigan-Spectre had problems with the Joker only due to the fact that he was weakened from previous stories. Two issues prior to the Joker story, Spectre gets stabbed by the spear of destiny, and even the Joker issue itself says that Spectre is weakened.
Context's important, you know.
There's a Pre-crisis issue (DC Comics Presents #72), where Joker also managed to take possession of Maaldor's powers, and his control over that power was greater than Maaldor's simply due to his sheer level of insanity. Thing is, Maaldor was a multiversal power in that issue, he was actually threatening the whole multiverse, and pre-crisis we all know that means infinite universes.
Depends on which comic you're going with. For instance, in Detective Comics #664 (Knightfall) Scarecrow tried to uncover Joker's phobia to no apparent effect; in Titans, he apparently had a fear but nothing specific was mentioned. But yeah, one could say that his biggest fear is not to have Batman around; this was after all the reason why he couldn't kill him in Emperor Joker and kept on re-creating him. And in Batman LTDK #65 he supposedly kills Batman (although he's later revealed to be alive, but point is, Joker actually thought that Batman was finally dead) and when he does so, (in the next issue) he actually becomes sane and goes on to have a girlfriend for 3 months looking like a perfectly normal and sane person.
What i was referring to happened in a tie-in not in the main 6 issue arc (minus Secret Files & Origins), that's why perhaps you don't recall it. Here's the scan which outright states it:
Edit: I couldn't name everyone that Joker jokerized by that time, since there are too numerous, but it was definitely global. That tie-in takes place after Joker Last Laugh #3, where that's how we see the Earth: