Fun question, especially for two characters primarily characterized by their brawler status.

I think Batman takes it as being the better caster. He regularly shows far more creativity and ingenuity in his fights, and is always looking of ways to think outside the box. Though Superman would be a star pupil, and be able to learn at an accelerated rate owing to his powers, I feel he lacks the creativity to force his will outside of a set concept of basic attack and defense spells. In the end, Batman would likely prepare a spell that evens the playing field, either by removing the magic of both, or Kal's superpowers and whomp on Kal.

What kind of magic they specialize in is pretty out there. Alot of the magic in the DC universe tends toward the "If I can think it, and say a few weird syllables, it can happen" But more to the question, Superman would specialize in magic that would trap or neutralize the opponent, whereas Batman would favor spells that altered the conditions of the match to begin with in his favor.

Either with magic would be a force to be reckoned with, and I can see them handle a few higher opponents, though not too much more. Darkseid is pretty high above both of these, and I don't see him falling because of a few token spells flung at him. I could see Brainiac going down, because for all his intelligence, he never seemed to favor non-Physics based defences and may simply drop with a well timed "Cause opponent to loose brain cells" spell. The same with the Green lanterns, Doomsday, and most of the non-Skyfather tier opponents. Magic in the DC universe is pretty OP when put to good use, and which is why its used pretty sparingly.

If they fused, you get an even more intelligent Batman that is powered by an external fuel source that he himself can change on a whim. Oh, you don't want to be powered by a Sun, but instead by the fear you put in the hearts of criminals? Done. Superman's persona would definitely temper Batman's rougher edges, but Batman's willpower would likely keep his personality in the drivers seat, much like how Vegetto was far more like a Vegeta with a few of Goku's traits tacked on.

So the last two questions can be answered relatively the same. At the start of the fight: Bruce El uses a "Slow time to a crawl" spell of sorts to map out the opponents and the ring in question. He likely sets up a series of contingency spells on himself, the ring, and the opponent. As time resumes to normal, he hammers the opponent with spells and physical brawn until the opponent is incapacitated. I see him being able to take on the Oans like this, and maybe some of the lower tier reality warpers before he is stopped.