The instructions I followed said to use a pint, so that's what I did. Less water would probably be somewhat better from a dilution viewpoint, but it's still only 1/8th of a gallon, and the amount of dissolved sugars more than offset the additional water in terms of overall gravity. Probably best to just use as little water as you can use without burning your priming sugar.
Probably better to let it cool from a yeast health standpoint, better to put it in quickly from a contamination standpoint. What I did was put it in my sanitized bottling bucket more or less right away and then slosh it around to let the cool plastic leach off as much heat as was practical before beginning to siphon my beer. If you think about it, only the first little bit of the beer is going to be exposed to heat that is actually damaging, the vast majority will be going into the only slightly warm mix of the early siphoned beer and priming sugar water. Once again, I can see how using less water would be beneficial here as it would contribute much less heat to the overall batch.
