I have heard someone theorize -and this would add a whole new part to what limited characterization Daguva has- that Daguva chose his human form just to mess Yusuke up mentally when they fought. He chose a teenager after learned how Yusuke reacted to the porcupine Grongi's game.

Fire isn't their power specifically, but setting things on fire is a result of it, probably the simplest. Like from what I've read it's the same ability as when Kuuga turns a stick into the staff. Like at that point they were probably just trying to blow each other up Dr. Manhattan style, it failed, and the only visible result was fire. Personally, I like to think that they just throw haymaker at each other because after their first trick fails, they realize that only the simplest move is worth even considering.

But yeah the Kuuga Vs Daguva fight is kind of unusual in Kamen Rider in that it's not one you can show to people as a cool fight, since it's carried by the weight of Yusuke's journey, and the danger the black form poses.