1. It won’t exactly kill him, but it’s highly recommended that you avoid submerging the tip of his tail, as doing so would be a risk to his life. While there isn’t exactly a product out there specifically designed to do this, you might be able to fashion a floatation device that can be placed around his tail close to the flame on its tip to keep it upright and out of the water. Alternatively, the kiddie pool idea would work, but always be sure your charizard’s tail remains outside of it.
2. The bad news is yes, an eevee’s body temperature does indeed drop upon evolution into a glaceon. The good news is it doesn’t drop to a point where a glaceon can’t safely be cuddled. Just be wary of any signs that he’s getting overheated, and he should be fine.