Why does Saltan get married that hastily? Because there is a war going on (in Pushkin's text, it's stated that it has already started by the time Saltan got married; in the opera, Militrisa's words imply that the war per se began three weeks after the wedding, but even in that case, Saltan could most probably see beforehand that a conflict was brewing). He knows he has to go to fight personally soon, so he needs to secure the succession, and fast, in case he gets killed. That's also why he picks the girl who promises to give him a strong heir rather than either of her sisters, even though they promise to be Royals Who Actually Do Something.
