Here's an interesting what if. Suppose that sometime in 1910, Emperor Franz Josef Ferdinand dies. What happens next? Does Archduke Franz Ferdinand take the throne, or will there be a succession crisis?
Just as an opening statement, the Kaiser personally visited Bosnia between the May 30 and June 5 (that was the plan, although he returned to Vienna on June 3). The tour included several stops to meet the people on train stations and Serb anarchists (according to a police informant) planning an assassination attempt in Mostar (which Franz Josef dismissed as unlikely, reasoning that any attempt would be made in Sarajevo, not Mostar; he was also rather dismissive of the risks and security measures, claiming that it's a risk that comes with the job). IIRC, there was an actual assassin, but he failed to take action ... but don't take my word for it, I'm fuzzy on the details. So, if you're looking for a plausible way to off the old guy, that's the primary option.
Now, moving on. Franz Ferdinand didn't have any real competition to the throne, so he'd get it by default. The issue comes from FF's little ideas on how to deal with Hungary, which, IIRC, included not accepting the Hungarian crown, plans for centralization and abolishment of the dual monarchy system, as well as a desire for a 'dictatorship from the centre' in order to stabilize the Empire. His wife wasn't popular among the court, but that had little effect otherwise, especially after the old Kaiser stood up for her.
I should note that, in regards to his reform plans, Franz Ferdinand did, at one point, remark that it was likely he wouldn't be Emperor long. Hopefully, long enough to ensure the survival of the monarchy.
His words, not mine (though I may have paraphrased a bit).
Would this cancel out World War I?
Hardly, if anything, it might trigger it. Albeit in a different manner. Keep in mind that the network of alliances was already in place by that point, which means a single spark could set all of Europe ablaze.
And say what you will, Franz Ferdinand didn't have plans to be subtle or restrained.
What sort of relations would (should he take the throne) Franz Ferdinand have with the other monarchs of Europe, and what sort of path may Austria-Hungary take under his guidance?
Pro-German, anti-Italian, well received in Britain. His relations with Wilhelm II were friendly, to the point where Wilhelm was considering passing Elsass-Lothringen to Franz Ferdinand so his children could have an inheritance (thereby making it a federal state), since FF's children were banned from the throne as a result of his marriage. I'll not that that's unlikely to affect things much, as both Karl and, later on, his son Otto were available and there was no shortage of other Habsburgs.
Anti-Italian, well, FF really didn't care for Italy, viewing it with contempt as an ancestral enemy of Vienna. If he ascends to the throne, expect a major cooling in the relations between the two countries, especially as FF was even more averse to compromise than Franz Jozef.