Well, at 1462 only one of Mehmed's sons was capable of the throne - Bayezid was 15 and Cem was 3. An early death would have meant that Bayezid's claim became much more secure. I don't think the fact that Bayezid ascended the throne at 15 is a problem since Mehmed II himself took the throne (first time) at 12. Not sure that Bayezid would have had the nerve to kill Cem, though (unlike, say, Selim I) - but by the time Cem was of age Bayezid might well have consolidated enough power to make this a moot point.
Vlad's killing of Mehmed would have been hailed across the Christian world and perhaps even would have led to another Crusade...
if Europe hadn't been focusing on the Hussite heresy in Bohemia. The crucial component of any Ottoman Crusade - Hungary - would probably have considered crusade against Bohemia more fruitful than crusade against the Ottomans. So I don't think another Varna Crusade could have gotten through.
Have to say that Bayezid II was quite competent at consolidating the Empire, if not expanding it. An earlier Bayezid might have been more cautious about expansion, probably focusing mostly on the Venetians and Genoans rather than everywhere at once (though events out of his control, like the Bosnian revolt, might have forced his hand). Maybe more time might also have allowed Bayezid to deal with the succession/retire early, so that he could hand over a strengthened 'core' Ottoman Empire to Selim I (and he frankly should, given Selim's capabilities

).