Like Bee said, you won't have the leave the Park/have your RP ended. Your Ranger might either have you try and help put it out, or escort you to another section of the Woods. Maybe your Ranger and the Ranger of the person responsible (if it was someone else) would somehow get in touch in the RP, and you'd go to help out. There are all sorts of things that could happen, but like Bee said, unless you started the fire on purpose, it wouldn't end your current visit.
Yes, if you could do them for me that'd be so very awesome.
Also, made an edit to the Team RP thing: If a Trainer decides to catch their teammate's unwanted Pokemon, they'll randomly lose one of their own encounters so they don't end up getting extra encounters.
I'll add these things to the Parkpedia as Bee suggested, I suppose.