Assert.AreEqual(414, Kata.NextBiggerNumber(144)); => Expected: 414 But was: -1
4 and 4 is the same, it should return -1, since it has already the "biggest possible" value.

No, 144's digits can be reordered to get a bigger number, and that is the expected value 414 (the biggest value would be 441, but that's not what the kata ask, it asks for the next bigger value).

Expected: 1234567908

But was: 1234567809

For that my guess is original value was 1234567890

Why don't you write the input to the console to see what it is?

I have no clue what you are meaning here: can you rephrase?

Also, specifying the language of the issue and some more details about it might help.