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Honestly, I think John Lithgow would have been amazing as The Joker.  Before I even saw this list I had him in mind as a possible alternative Joker to Jack.
Nicholson was brilliant, and I don't think anyone could be as memorable or as funny as him in the role (even Heath Ledger).  His delivery of much of the film's dialogue makes Batman '89 one of the most quotable films in cinema history as far as I'm concerned.
However, I do think that Lithgow would have given us a Joker closer to that of the animated series, i.e. sinister, vicious and scary.  Lithgow is tall, lanky and has just the right supercillious, mocking tone to his voice.
I also think that Tim Currey would have made an effective Joker, especially in view of his roles in 'It' and 'Legend'

Keaton's Bruce Wayne probably learned martial art skills from the same people who taught Bale's Bruce Wayne, i.e. Henry Ducard, his mentor (irrespective of whether he was actually Ras Al Ghul or not).
Bruce Wayne's a billionaire, so it would not be very difficult for him to collect various artefacts from throughout the world.  I imagine that he collected them as 'research' for his own costume and armour pre-Batman.  Alternatively, he might just be a freak with a military history obsession.

Another thing that leads me to believe that Batman has not been cleared by the end of Batman Returns (if we are going by the novelizations) is that there is reference to Harvey Dent helping to clear Batman's name in the 'Batman Forever' novelization.
Like Batmoney suggests, the way Bruce behaves at the end of Batman Returns also suggests that he has been coping with Selina's disapperance for a few days.

That may be the case, but Gordon was not the most powerful man in Gotham.  I can't imagine the Mayor or the families of the victims sharing his point-of-view and letting the issue rest.  In fact, as the virtual riots that occurred after Batman was framed demonstrate most of the public seemed to regard him as public enemy no.1.  As level-headed and reasonable as Gordon is, the public hysteria and the public officials' self-serving response would probably seek to demonise Batman for as long as possible.  At least until he was officially cleared.  It's the same kind of behaviour we see in society every day (just think of how the press/mass public act after a given terrorist incident).

Not sure if you meant that as a joke, but that was actually quite a reasonable suggestion.  Although I suspect Batman was far too intelligent to fall for that.

You're right.  The novelization does state that the two events occur right after each other, but from the watching the film it always seemd to me that the police would first need some time to clear Batman of the crimes pinned on him before they would start reusing the Bat Signal.  Also, I can't imagine Catwoman would be able to recover so quickly and prepare a whole new costume within the space of a few hours (of course, the appearance of Catwoman occurred in the film as an afterthought when all the principle filming had been completed).

I always assumed that the final scene in the film took place a few days after Batman's tussle with The Penguin, Catwoman and Max Shreck inside Arctic World.  Batman was still essentially a vigilante during his final fight with these villians, so it would be unlikely that Commissioner Gordon would have switched the Bat Signal only moments later.
I suspect that during the days that intervened between Batman's fight with The Penguin, and the scene in which he is being chauffeured by Alfred, Commissioner Gordon and his men had fully charged and interviewed the remaining members of The Red Circle Triangle Gang (including the ones Batman had apprehended himself).  I also suspect that they're interviews will have exonerated Batman for the murder of the Ice Princess and the Batmobile's rampage through the city thereby restoring the city's confidence in him.