Saffron's power is so immense already that the amount it is boosted by the Kinjakan is practically insignificant.
In your opinion. In my opinion it made his blasts significantly more powerful. The blasts done without the aid of the staff were not as powerful. Also the full abilities of the staff are never shown it could very well have the power to throw balls of heat. We can't know that since in Saffron's hands it would have just looked as if Saffron alone were throwing them and can't judge by Ranma not throwing balls of cold air since Ranma did not really know how to use the staff (he thought he broke it while it actually turned on) and possibly didn't think of using it in that manner.
Cologne herself calls it the Body of Ice. As for how cold it is, I really think you're overanalyzing everything here. If the Body of Ice generated that much cold, Takahashi would have made it more obvious I think. To survive Saffrons ultimate attack, Ranma had to freeze himself solid with the Gekkaja. Ranma has never done anything even remotely that powerful with the Body of Ice.
As for the phoenix pill, while that did give Ranma extra heat resistance, it only brought his resistance up to his previous limit, because the Full-Body Cat's Tongue was never actually cured.
In the translation I had last looked at it did not have her call it the body of ice. That's one of the problems with reading multiple translations it is hard to keep track as to which one is the one being used. (I've read multiple translations and have started on the original Japanese but that is really slow going for me.)
As for over analysizing isn't that what basically everyone is doing?
Takahashi didn't have any reason to make it obvious, or tell how cold it was except for a comment by Ryoga saying so cold, and she did not go into details with a lot of the things in the manga since it was not needed for the story. Ranma also (as far as we know) has never tried to use the body of ice in any form other than in the Hiryu Shoten Ha, he maybe able to freeze himself solid (though it probably would take longer without the staff and would not have helped him at any other point in the manga - lots of techniques he may know might not have been shown because a situation in which the techniques would benefit him did not appear - like the breaking point Ranma may know it but there was no point in the manga in which it would have benefited him to use it) or use it in other forms if he wanted to we have no way of knowing (personally I'd use it to chill drinks if I had the ability to use it). Though he was frozen when he had Happosai's super cold.
Full body cat tongue was a pressure point. Pressure points wear off. It is possible that the pressure point wore off at some time before the battle with saffron (whether it did or not is unknown).
as long as you aren't a Deamon or Kaiju they will take it as normal.
They may very well not be overly bothered by those showing up after awhile, Taro's cursed form is a Kaiju.