There are plenty of places to stay around Pucon, and several around the Fu. We drove toward the town of Futa from the river and stayed at a great place called Camping Loncanao. It had refugios (indoor places to cook and even sleep), they provided firewood, and it had hot showers all for something like $3 per person per night.
Environmentally, bugs can be bad - especially giant mutant horseflies.
I don't remember any poison oak.
It snowed on the tops of the mountains while we were at the Fu late last January, and sleeted a bit at river level. Although the water wasn't super cold, I was glad to have a drysuit.
We drank the water most everywhere and it was fine.
Cars and kayaks are available for rent in Pucon.
I wouldn't count on paying for anything with a credit card at the Futa - bring cash. There are no working gas pumps in Futa or Chaiten, so fill up before you go down there, and maybe carry some bottles with extra. You can buy small bottles of gas in Futa, but they don't always have it in stock and it's crazy expensive that way.
Good luck, and have fun down there!