Would it be unethical to create an A.I. bot that has full advantage of ALL of the game mechanics? Would it be better if it was optional and gave full disclosure before it let you face this opponent?
Starting of with if it was not optional and the player did know: If I was playing through a game and in the final level the opponent was humanly unbeatable I would feel cheated in the same way I would if I bought a jigsaw with a piece left out by design.
If it was not optional and the player didn't know: This is similar to above, but the player will in some ways waste their time trying to achieve the impossible.
If it was optional and the player didn't know, then it's really a time waster.
If it was optional and the player did know then I don't know what it would do for the game other than an Easter egg or for narrative.
Some games have arguably unbeatable elements:
any endless mode, here there will be a truly unbeatable stage however only a perfect player will be able to reach a level where perfect play will still be defeated. All other levels you see can be beaten.
in the game splunky a ghost will appear and chase the player if they take too long to finish a level, this is unbeatable in the sense that it can't be stopped or defended against but it is beatable in that you can outrun it.
in many games you will see your final opponent at an early stage and after being killed you will progress to the next level. But it is always the case that you win in the end.
Would it be unethical to create an A.I. bot that has full advantage of ALL of the game mechanics?
Probably. (I would say Yes, considering you make a perfect A.I.)
Just like the comments say; If your A.I. takes full advantage of every mechanic in the perfect way, you can never beat it.
Have you seen this answer / post? It is about building in a handicap into an A.I. but the answers also describe why a perfect A.I would be unbeatable.
I think this post will also answer your second question.