Tell me how turn based battling would work?

Same as before? Or you'd get a quest saying, "Defeat this NPC Trainer by the arcade" you go to the gym and you get your own instance. If you have a party, they can go inside and watch, maybe offer advice on the next moves. If it is PVP, just randomize who gets the first move. For advanced players, put a countdown timer each move to keep the action going.

Could you upgrade your character?

I don't see why you couldn't...like at all.

If you change either of those, it basically wouldn't be a Pokemon game anymore.

No? I've only played red/blue, and then emerald many years later. I'm sure the games have seen significant changes since then. And they definitely felt changed up a bit since the red/blue days. Maybe it shouldn't surprise anyone that there will be some differences between the handheld games, the trading card games, and a PC MMO. Doesn't mean it stops being Pokemon at all.

Once you make the MMO, do you stop making the actual games?

Again, no? You'd have an entirely different team running it. Doesn't mean it couldn't be faithful to the source material. I doubt Nintendo would just hand the opportunity over to some low-budget company that has never heard of the game before. And it's not a wildly complicated system to begin with.

Pokemon was literally designed to be able to play in very short bursts, so the exact opposite of that would be a MMO.

This is really nonsensical. Can you provide any sources that indicate children/teens/adults play Pokemon for only short bursts? I'm pretty certain that people who play the handheld pokemon games play it just as long as any other game.

Also, why do you think everyone is crying these days about MMO's turning more casual? Hardly any these days require you to play for more than even an hour or so. They know this is the generation of the mobile game user and people want instant gratification. Things move quicker now and so you can absolutely play an MMO in short bursts if you wanted. I've been doing that for a decade now. It's easier these days.

If you don't want it, just don't play it. There's no way it'd impact the handheld games. In fact I believe this is probably the only franchise that would be able to rival WoW in subscription numbers. If it were released tomorrow for $9.99 per month and was a solid game, it'd easily take 2nd place over Star Wars, Final Fantasy, GW2 and ESO in a heartbeat. They'd be stupid not to at this point.