I'll try and give advice where possible.
2. There are various factors you want to consider. Will the battle be inside the actual gym itself, what does the battlefield look like, what do the moves look like and act like, besides doing damage/inflicting an aliment.
For a little bit of an example, here's a small bit from a fanfiction I'm currently writing about the manga version of Pokemon:
Red was first to attack. "Poli, use Ice Beam!" Poli put his fists together and a frozen spear flew at Peesk.
"Peesk, fly up!" Yellow ordered. Peesk beat his wings quickly, dodging the frozen spear with ease. "String shot!" The white thread wrapped around Poli, binding him on the spot.
"Strength!" The veins on Poli's arms popped and he burst the string.
"Peesk, Poison Powder!" Peesk flapped his wings and a purple haze filled the field. It grew thicker and eventually, Red and Poli couldn't see anymore.
The haze moved quickly, "Quick, back off Poli!" Red ordered. Red and Poli jumped back, hiding themselves behind some nearby trees. The haze cleared but Yellow and Peesk were nowhere to be seen. Where'd they go?
"Confusion!" Red looked up, his opponents were above him, standing in the tree's branches. Poli was covered in a violet light and his eyes became swirled.
Red weighed his options, and then held up Poli's Pokéball. "Return!" Red replaced the ball and tried to decide who was next. "You're better than I thought."
Yellow smiled, dropping from the tree with Peesk easily, the movement very natural to her. "Thanks. But you shouldn't underestimate your opponents."
3. Personally, I wouldn't keep reading if there were two battles right after each other. It would get a little boring, unless you described how the gym leader kicked both of their butts during the first challenge XD
4. Throwing the hero into an evil plot he discovers by accident. That's pretty much how all stories are formed. It's not bad at all. I mean, a story would lose interest if there wasn't some sort of problem. The whole thing is about how you have the character discover this problem and what the actual problem is.
5. Detail is NECESSARY. However, you need to find the right amount of detail to put into the story. Taking a whole page on describing how a character looks is an example for too much detail. I think you should still have some detail about the battles, just not bother to include too much about what happens. However, since this is a Pokemon fic you're writing, you're going to need some amount of detail.
So, is the story still on your computer, or posted on the site somewhere? I'd like to see how it's coming along.