The mere fact that there is wide disagreement about some ethical questions doesn't help the argument (as some people think), because there are all sorts of very controversial questions where it's still commonly accepted that these questions have a correct answer.
No, the vast majority of people don't think there's a singular set of correct ethics, and especially not one where "eating octopus is unethical" is a tenet.
I agree that maybe most people believe in objective morality, but moral relativism exists and I don't think that it's so unpopular that it's insignificant.
The moral system is unrelated to their scientific advice.
It also doesn't cover the "don't eat X animals" part, as even for their society (e.g. USA) that's debatable ethically, and not something the generally acceptable moral system holds.
Yes.
At a minimum, they shouldn't state their "own opinion from their own ethical context" as some kind of universal fact: "it's not only deeply unethical (...) scientists say".