Very nice piece, thanks. Also posing some problems at the end is a great thing!

As to 1. — The entire explanation is conveyed in Wittgenstein’s Lecture on Ethics. He considers exactly your question and answers it in the negative. I strongly encourage you to read it.

As to 2. — I think that it was never said that there is only one possible moral intuition and that it’s neverchanging. In fact, history gives us a plethora of examples of differing moral intuitions towards the same questions throughout time. This might account for subjectivity of moral attitudes, which indeed are unfeniable.