Not a specialist in these by any means, but a collector of interim issues worldwide when I find them.
How was the sky inked in?
The litho screen in the top stamp shows it started with a photographic negative. You can look up how the lithographic printing plate is created. For the "night sky" type, I suspect the negative or even the original artwork was retouched by hand. There's a lot more changed besides, like the bottom line of the river, the top of the volcano/mountain, a partial figure at the front of the carabao, etc.
Perhaps to try and improve the design or maybe try to fix a bad negative to make a new printing plate. The carabao are clearer here but they did fail on other parts of the design.
What do you do about CTO stamps?
In this case, I would collect them and label them as such. This seems to be like other areas where postally used is very much harder to find in many cases. There are also favor-cancelled items which can be hard to tell from postally used. Overall, it's a matter of personal preference.
If you have a CTO stamp that is not one of the ones "known only as CTO", is it inappropriate to put it in your collection?
Again, a matter of personal preference. You at least want to try to make sure you don't have a forged cancel, though.
Is there any point in getting a cert?
It depends. You are paying for a service, and if something is (so far) unique, you could get a "no opinion" back, obviously. For the stamp above, does the written part match the violet/violet surcharges? Then I would say it has a definite shot.
If it's genuine, can I say anything other than "I have a genuine stamp that's not in the catalogue"?
What else would you want to say or could say? If this is from ex-SoandSo's collection, that could be useful.
When can you say I have the only reported stamp? For that matter, when you read about a stamp as being one of only 2 known, or 1 of 4 known, who exactly is keeping track of these things?
I would use weasel words like "currently the only reported stamp as far as I have been able to determine" or somesuch. It has to first be proven to be genuine or have experts assert that it is; there's the rub.
It's usually the author of an article maybe quoting some other source or being part of a specialist group. And if it's an older source, that number can change and change dramatically over time.